How come Almalexia, Vivic, and Sotha Sil had to renew their powers through the heart of Lorkhan every so often or they'd lose their divinity?

Maybe they used up/exhausted their bodies/powers?

Cos they borrowed their divinity, rather than stole it. Their path to godhood was a temporary one, tapping into the power of Lorkhan and renewing it whenever it faded. They didn't commit to a more permanent form apotheosis like mantling/CHIM.

One might argue that ALMSIVI tried to mantle the three 'Good Daedra', but I don't think that was the case. They didn't try to "walk like them". The Tribunal insinuated that it was actually the Princes who walked like them and Boethiah, Azura and Mephala were simply articulations of their beings before they themselves took form. The warm-up act to The Three's grand show.