user3831: I have just played a thoroughly enjoyable game, where in the middlegame I was forced to give up the queen for two minor pieces and defend. After 30 moves and some trades, the situation got simplified to following position:
[fen "8/4k3/2p5/3p4/1P1q4/3N4/2P5/2KN4 w - - 0 0"] 

 1. Kd2 Kd6 2. N1b2 Qh4 3. Na4 Qh6+ 4. Kc3 Qf6+ 5. Kb3 Qf7 6. Nac5 d4+ 7. Kb2 Qc4 8. Ne4+ Kc7 9. Kc1 Qd5 10. Nec5 Qg5+ 11. Kb2 Kb6 12. Kb3 Kb5 13. Kb2 Qd5 14. Nb3 Qc4 15. Nbc5 Qc3+ 16. Kc1 Kc4 17. Kb1 Qa3 18. Ne4 Qa8 19. Nd2+ Kc3 20. Ne4+ Kc4 21. Nd2+ Kd5 22. Nb3 Qa3 23. Nbc5 Kc4 24. Ne4 Qa8 1/2-1/2

As you can see, the game went further on for some 25 moves; I managed to hold the position and the game ended in a threefold repetition.
As far as I can tell, with correct play by white, black should not be able to make any progress. Is that really so? (EDIT: Just to clarify, I seek some conclusive analysis, not merely a yes/no statement)

user2042: White defends, but it is really a pain to hold this position. It took me few minutes to formulate correct plan since Stockfish found some strong ideas for Black. 
Below is the image of the fortress we are aiming for:

If Black king tries to penetrate through queenside, he must aim for c3 square in order to create double attack on c2 pawn (using king and queen). We stop that plan with timely Na4+, which pushes the king back.
If Black tries to penetrate to b1 with the king ( through queenside ), hoping to win the c2 pawn ( queen + king create double attack on the pawn) White will be in time to reposition Nc5 to e2, blocking black queen's attack along the second rank, thus defending by simply moving the king to d2 and d1.
The last option for Black is to get to d1 or d2 with the king, but White manages to reposition Nc5 to d2 which creates impenetrable fortress since both knights control so many important squares (e5, e4, f4, f3, f2, f1), effectively cutting off the black king. White can also move the king to b1 and push out black king with timely Nb2+, in case he is late to reposition the knight to d2.
The whole point is that we must reposition Nd1 to c5, after which White defends. 
Since analysis is very lengthy, I will post an illustrative game I played against Stockfish. Other important ideas will be shown in sublines. 
If you need further questions leave a comment and I will update my analysis.
[Title "AlwaysLearningNewStuff vs Stockfish"]
[FEN "8/4k3/2p5/3p4/1P1q4/3N4/2P5/2KN4 w - - 0 1"]

1. Kd2 Qg1 (1...Ke6 2.Nc3 Kf5 3.Na4 Ke4 4.Nac5+ Kf3 5.Nb3 Qe3+ 6.Kc3! Ke2 7.Kb2 Kd1 8.Kb1! Qe2 9.Nb2+) 2. Nc3! d4 3. Ne2 Qe3+ 4. Kd1 Ke6 5. Nec1 Qg1+ 6. Kd2 Qh2+ (6...Kf5 7.Nb3 Ke4 8.Nbc5+ Kf3 9.Ne5+ Kf2 10.Ned3+ Kf1 11.Kc1! Ke2+ 12.Kb2 Kd2 13.Nb3+ Kd1 14.Kb1! Qg2 15.Nb2+!? Ke2) 7. Kd1 Kd5 8. Nb3! Kc4 (8...Ke4 9.Nd2+ Ke3 ?? 10.Nf1+ Ke4 11.Nxh2+-) 9. Nbc5! $8 Qg1+ 10. Kd2 Qe3+ 11. Kd1 Kc3 12. Na4+ $8 Kc4 13. Nac5 Qg5! 14. Na4 $7 Qg1+ 15. Kd2 Qg5+ 16. Kd1 Kb5 17. Nac5 $8 Qg1+ 18. Kd2 Kc4 19. Na4 $8 Qe3+ 20. Kd1 Kb5 21. Nac5 Kc4 22. Na4 Qg5 23. Nac5 Kb5 24. Nb3 Ka4 25. Nbc5+ Kb5 (25...Ka3 26.Nb3! Qg1+! 27.Ke2! Ka2 28.Nd2! Qe3+ 29.Kd1 Qe6! 30.Kc1! Qh6 31.Kd1 Qh1+ 32.Ke2) 26. Nb3 Qe3 27. Nbc5 Qg1+ 28. Kd2 Qg5+ 29. Kd1 Qh6 30. Nb3 Kc4 31. Nbc5 Qh1+ 32. Kd2 Qf1 33. Na4 Qg1 34. Nac5 Kd5 35. Ke2 Qg2+ 36. Kd1 Qh1+ 37. Kd2 Kc4 38. Na4 Qh6+ 39. Kd1 Kb5 40. Nac5 Kc4 41. Na4 Qg5 42. Nac5 Qh4 43. Kd2 Qh6+ 44. Kd1 Qh1+ 45. Kd2 Qa1 46. Ne4! Qa7 47. Nec5 Qa1 48. Ne4 Qf1 49. Nec5 Kd5 50. Na4 c5 51. bxc5! Qg2+ 52. Kc1! Qg5+ 53. Kb2 Ke4 54. Nb6! Qd2 55. Kb1 Qg5 56. Nc4! Kd5 57. Nd6! Qg1+ 58. Kb2 Qg4 59. Kb1 Qd1+ 60. Kb2 Qg1 61. Ka2 Kc6 62. Kb2 Kd5 63. Ka2 Qh1 64. Kb2 Qd1 65. Nb5 Qg1 66. Nd6 Qd1 67. Nb5 Qf1 68. Nd6 Kc6 69. Nc4 Qd1 70. Nd6 Qd2 71. Kb1 Kd5 72. Kb2 Qh6 73. Kb1 Kc6 74. Kb2 Kd5 75. Kb1 Kc6 76. Kb2 Qh1 77. Ka2 Qg1 78. Kb2 Qg8 79. Kb1 Kd5 80. Kb2 Qh7 81. Kb1 Qh6 82. Kb2 Kc6 83. Kb1 Qg7 84. Kb2 Qh6 85. Kb1 Qh7 86. Kb2 Qh1 87. Ka2 Qh4 88. Kb2 Kd5 89. Ka2 Qh2 90. Kb2 Qh1 91. Ka2 Qd1 92. Kb2 Qf1 93. Ka2 Qf3 94. Kb2 Qh1 95. Ka2 Ke6 96. Kb2 Qd1 97. Nc4 Kd7 98. Nd6 Kc6 99. Nc4 Kc7 100. Nd6 Kb8 101. Nc4 1/2-1/2


3831: <p>I have just played a thoroughly enjoyable game, where in the middlegame I was forced to give up the queen for two minor pieces and defend. After 30 moves and some trades, the situation got simplified to following position:</p>

<pre><code>[fen "8/4k3/2p5/3p4/1P1q4/3N4/2P5/2KN4 w - - 0 0"] 

 1. Kd2 Kd6 2. N1b2 Qh4 3. Na4 Qh6+ 4. Kc3 Qf6+ 5. Kb3 Qf7 6. Nac5 d4+ 7. Kb2 Qc4 8. Ne4+ Kc7 9. Kc1 Qd5 10. Nec5 Qg5+ 11. Kb2 Kb6 12. Kb3 Kb5 13. Kb2 Qd5 14. Nb3 Qc4 15. Nbc5 Qc3+ 16. Kc1 Kc4 17. Kb1 Qa3 18. Ne4 Qa8 19. Nd2+ Kc3 20. Ne4+ Kc4 21. Nd2+ Kd5 22. Nb3 Qa3 23. Nbc5 Kc4 24. Ne4 Qa8 1/2-1/2
</code></pre>

<p>As you can see, the game went further on for some 25 moves; I managed to hold the position and the game ended in a threefold repetition.</p>

<p><strong>As far as I can tell, with correct play by white, black should not be able to make any progress. Is that really so? (EDIT: Just to clarify, I seek some conclusive analysis, not merely a yes/no statement)</strong></p>
 2042: <p>White defends, but it is really a pain to hold this position. It took me few minutes to formulate correct plan since Stockfish found some strong ideas for Black. </p>

<p>Below is the image of the fortress we are aiming for:</p>

<p><a href="https://i.stack.imgur.com/11SJE.png" rel="noreferrer"><img src="https://i.stack.imgur.com/11SJE.png" alt="enter image description here"></a></p>

<p>If Black king tries to penetrate through queenside, he must aim for <code>c3</code> square in order to create double attack on <code>c2</code> pawn (using king and queen). We stop that plan with timely <code>Na4+</code>, which pushes the king back.</p>

<p>If Black tries to penetrate to <code>b1</code> with the king ( through queenside ), hoping to win the <code>c2</code> pawn ( queen + king create double attack on the pawn) White will be in time to reposition <code>Nc5</code> to <code>e2</code>, blocking black queen's attack along the second rank, thus defending by simply moving the king to <code>d2</code> and <code>d1</code>.</p>

<p>The last option for Black is to get to <code>d1</code> or <code>d2</code> with the king, but White manages to reposition <code>Nc5</code> to <code>d2</code> which creates impenetrable fortress since both knights control so many important squares (<code>e5</code>, <code>e4</code>, <code>f4</code>, <code>f3</code>, <code>f2</code>, <code>f1</code>), effectively cutting off the black king. White can also move the king to <code>b1</code> and push out black king with timely <code>Nb2+</code>, in case he is late to reposition the knight to <code>d2</code>.</p>

<p>The whole point is that we must reposition <code>Nd1</code> to <code>c5</code>, after which White defends. </p>

<p>Since analysis is very lengthy, I will post an illustrative game I played against Stockfish. Other important ideas will be shown in sublines. </p>

<p>If you need further questions leave a comment and I will update my analysis.</p>

<pre><code>[Title "AlwaysLearningNewStuff vs Stockfish"]
[FEN "8/4k3/2p5/3p4/1P1q4/3N4/2P5/2KN4 w - - 0 1"]

1. Kd2 Qg1 (1...Ke6 2.Nc3 Kf5 3.Na4 Ke4 4.Nac5+ Kf3 5.Nb3 Qe3+ 6.Kc3! Ke2 7.Kb2 Kd1 8.Kb1! Qe2 9.Nb2+) 2. Nc3! d4 3. Ne2 Qe3+ 4. Kd1 Ke6 5. Nec1 Qg1+ 6. Kd2 Qh2+ (6...Kf5 7.Nb3 Ke4 8.Nbc5+ Kf3 9.Ne5+ Kf2 10.Ned3+ Kf1 11.Kc1! Ke2+ 12.Kb2 Kd2 13.Nb3+ Kd1 14.Kb1! Qg2 15.Nb2+!? Ke2) 7. Kd1 Kd5 8. Nb3! Kc4 (8...Ke4 9.Nd2+ Ke3 ?? 10.Nf1+ Ke4 11.Nxh2+-) 9. Nbc5! $8 Qg1+ 10. Kd2 Qe3+ 11. Kd1 Kc3 12. Na4+ $8 Kc4 13. Nac5 Qg5! 14. Na4 $7 Qg1+ 15. Kd2 Qg5+ 16. Kd1 Kb5 17. Nac5 $8 Qg1+ 18. Kd2 Kc4 19. Na4 $8 Qe3+ 20. Kd1 Kb5 21. Nac5 Kc4 22. Na4 Qg5 23. Nac5 Kb5 24. Nb3 Ka4 25. Nbc5+ Kb5 (25...Ka3 26.Nb3! Qg1+! 27.Ke2! Ka2 28.Nd2! Qe3+ 29.Kd1 Qe6! 30.Kc1! Qh6 31.Kd1 Qh1+ 32.Ke2) 26. Nb3 Qe3 27. Nbc5 Qg1+ 28. Kd2 Qg5+ 29. Kd1 Qh6 30. Nb3 Kc4 31. Nbc5 Qh1+ 32. Kd2 Qf1 33. Na4 Qg1 34. Nac5 Kd5 35. Ke2 Qg2+ 36. Kd1 Qh1+ 37. Kd2 Kc4 38. Na4 Qh6+ 39. Kd1 Kb5 40. Nac5 Kc4 41. Na4 Qg5 42. Nac5 Qh4 43. Kd2 Qh6+ 44. Kd1 Qh1+ 45. Kd2 Qa1 46. Ne4! Qa7 47. Nec5 Qa1 48. Ne4 Qf1 49. Nec5 Kd5 50. Na4 c5 51. bxc5! Qg2+ 52. Kc1! Qg5+ 53. Kb2 Ke4 54. Nb6! Qd2 55. Kb1 Qg5 56. Nc4! Kd5 57. Nd6! Qg1+ 58. Kb2 Qg4 59. Kb1 Qd1+ 60. Kb2 Qg1 61. Ka2 Kc6 62. Kb2 Kd5 63. Ka2 Qh1 64. Kb2 Qd1 65. Nb5 Qg1 66. Nd6 Qd1 67. Nb5 Qf1 68. Nd6 Kc6 69. Nc4 Qd1 70. Nd6 Qd2 71. Kb1 Kd5 72. Kb2 Qh6 73. Kb1 Kc6 74. Kb2 Kd5 75. Kb1 Kc6 76. Kb2 Qh1 77. Ka2 Qg1 78. Kb2 Qg8 79. Kb1 Kd5 80. Kb2 Qh7 81. Kb1 Qh6 82. Kb2 Kc6 83. Kb1 Qg7 84. Kb2 Qh6 85. Kb1 Qh7 86. Kb2 Qh1 87. Ka2 Qh4 88. Kb2 Kd5 89. Ka2 Qh2 90. Kb2 Qh1 91. Ka2 Qd1 92. Kb2 Qf1 93. Ka2 Qf3 94. Kb2 Qh1 95. Ka2 Ke6 96. Kb2 Qd1 97. Nc4 Kd7 98. Nd6 Kc6 99. Nc4 Kc7 100. Nd6 Kb8 101. Nc4 1/2-1/2
</code></pre>
