In the 1931 championship Shoqeria Sportive played in Group A against Tirana and Bashkimi Shkodran collecting a win at home against Bashkimi Shkodran and three losses, with a negative goal difference of 4–9. Finishing last of the table meant that the team was relegated to the Kategoria e Dyte. Shoqeria Sportive was drawn to play for the next season in Group C of the "Kategoria e Dyte" against Leka i Madh Permet, Narta and Shqiponja Gjirokastër. The championship ended with success as the team was crowned champions of Group C and thus qualified for the play-off final against the Group B champion, Sportklub Kavajë. The one-legged tie ended 3–1 in favour of Sportklub Kavajë, which meant that Shoqeria Sportive remained for another year in the Second Division. In the next championship Nimet Abazi Delvinë and Vetëtima Himarë entered the competition, while Sportklub Narta withdrew. The season proved once again the superiority of the Red and Black team against their Second Division opponents, by finishing once again top of the Group C and securing promotion. In the two-legged final against Sportklub Elbasan, which determined the winner of the Second Division, Shoqeria Sportive lost 4–3 on aggregate, thus ending the season as runners-up.