I always thought Superman and Doomsday got less powerful, due to the strain.
I remember Superman making a comment that when he came back, it was as his power levels had diminished due to the fighting and beating he sustained.
In theory Billy has magical stamina, he's not dependent on solar energies.
Doomsday was getting stronger throughout the fight. Towards the end, Superman had to dig into his energy reserves in ways he had never done before, which allowed him to put Doomsday down, but also drained himself to the point of death in the process.