The following season the Albanian First Division was held in a knockout format, and they defeated KF Tepelena 1–0 on aggregate over two legs to progress to the second round, where they were beaten 14–4 on aggregate by Tomori Berat following 9–2 and 5–2 losses. In 1951, the ruling Party of Labour of Albania forced every team in the country to change their name and 24 Maji were to be called Puna, which literally translates to Labour, and in the 1951 Albanian First Division Puna Përmet as they were now called competed in Group 7 but did not progress out of the initial group stage. They did not compete competitively again until 1954 where they were put in Group 5 of the Albanian First Division, and once again not progressing past the first stage.
The following season, Albania's top league was played in a knockout format, with 24 Maji defeating KF Tepelena 1-0 on aggregate over two legs to advance to the second round. However, they were then eliminated by Tomori Berat, who won 14-4 on aggregate after losing 9-2 and 5-2. In 1951, the Albanian government mandated that all teams change their names, and 24 Maji became Puna. They competed in Group 7 of the 1951 Albanian First Division but failed to advance past the initial group stage.  They did not return to competitive play until 1954 when they were placed in Group 5 of the Albanian First Division, again failing to progress beyond the first round.