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, the Albanian First Division was played 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 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.