user8221: Today, when I was playing end game I had a queen, a rook and a king (no pawns). My opponent had just a queen. It was his turn (the board was pretty blank) and he started giving continuous checks. I tried to bring my pieces to defend the king but couldn't stop.
After sometime he claimed for a draw and argued that otherwise this would continue for ever (positions were not repeating, but still). I agreed.
So, is there any way to defend in such cases or is the match just over?
Even, is it fair that though we have a good lead the opponent is forcing a tie?
What would be the result if such thing happens in GM game?
Thanks, in advance.

user3819: According to theory, this endgame is won for the Q+R side. Note that you can afford a queen exchange, since K+R still wins against a lone K.
You should manage winning it (or reducing it by Q exchange) in less than 50 full moves which gives your oppenent the opportunity to claim a draw.

user-1: If the opposing king is in the center, and your king isn't in the corner, your goal is to pin his queen to his king as means of blocking a check (diagonal opposition). Move your king to force that bad check on his part. You should be able to win with KR v K. (Your goal is not to checkmate with two queens on the board, but to trade) It is a win with the queen, but to defend, check the opposite way from your king (If that makes sense).

user4362: This is called perpetual check and it is a draw. There is no extra rule for perpetual check because the draw can be claimed by invoking the three-fold repetition rule. (You said positions were not repeating, but if you cannot escape from a perpetual check, they will repeat sooner or later).
If you carefully go through the game, you will probably spot a possibility to prevent him from giving perpetual check. In that case you missed a win. Often you can manoeuvre in such a way, that at one point you can block a check by giving check yourself. But if you cannot find a way to escape from the checks a draw is a fair result and this is a common occurrence even in grandmaster games.

user4588: In the vast majority of the cases, an ending of Q+R vs. Q should be winning.
However, some exceptions exist, for instance: 


[FEN "6RK/7Q/5q2/8/8/8/8/3k4 w - - 0 1"]

      1.Qg7 Qh4+ 2.Qh7 Qf6+ 3.Rg7 Qd8+ 4.Qg8 Qh4+ 5.Rh7 Qf6+


In case you want to check whether your game was winning or not and how to win it, you can consult a tablebase, for example the free online tablebase of Shredder.

8221: <p>Today, when I was playing end game I had a queen, a rook and a king (no pawns). My opponent had just a queen. It was his turn (the board was pretty blank) and he started giving continuous checks. I tried to bring my pieces to defend the king but couldn't stop.</p>

<p>After sometime he claimed for a draw and argued that otherwise this would continue for ever (positions were not repeating, but still). I agreed.</p>

<p>So, is there any way to defend in such cases or is the match just over?
Even, is it fair that though we have a good lead the opponent is forcing a tie?
What would be the result if such thing happens in GM game?</p>

<p>Thanks, in advance.</p>
 3819: <p>According to theory, this endgame is won for the Q+R side. Note that you can afford a queen exchange, since K+R still wins against a lone K.</p>

<p>You should manage winning it (or reducing it by Q exchange) in less than 50 full moves which gives your oppenent the opportunity to claim a draw.</p>
 -1: <p>If the opposing king is in the center, and your king isn't in the corner, your goal is to pin his queen to his king as means of blocking a check (diagonal opposition). Move your king to force that bad check on his part. You should be able to win with KR v K. (Your goal is not to checkmate with two queens on the board, but to trade) It is a win with the queen, but to defend, check the opposite way from your king (If that makes sense).</p>
 4362: <p>This is called perpetual check and it is a draw. There is no extra rule for perpetual check because the draw can be claimed by invoking the <a href="https://en.wikipedia.org/wiki/Threefold_repetition">three-fold repetition rule</a>. (You said positions were not repeating, but if you cannot escape from a perpetual check, they will repeat sooner or later).</p>

<p>If you carefully go through the game, you will probably spot a possibility to prevent him from giving perpetual check. In that case you missed a win. Often you can manoeuvre in such a way, that at one point you can block a check by giving check yourself. But if you cannot find a way to escape from the checks a draw is a fair result and this is a common occurrence even in grandmaster games.</p>
 4588: <p>In the vast majority of the cases, an ending of Q+R vs. Q should be winning.</p>

<p>However, some exceptions exist, for instance: </p>

<pre>
<code>
[FEN "6RK/7Q/5q2/8/8/8/8/3k4 w - - 0 1"]

      1.Qg7 Qh4+ 2.Qh7 Qf6+ 3.Rg7 Qd8+ 4.Qg8 Qh4+ 5.Rh7 Qf6+
</code>
</pre>

<p>In case you want to check whether your game was winning or not and how to win it, you can consult a tablebase, for example the <a href="http://www.shredderchess.com/online-chess/online-databases/endgame-database.html">free online tablebase of Shredder</a>.</p>
