Assuming the spring dissolves perfectly (no breakage, just complete disintegration)
I think, eventually, this assumption breaks down. As the metal is dissolved away, the internal stresses in the spring will become greater than the remaining metal can hold, and the spring will break.
If the spring does eventually break, it will be a weaker spring since a lot of material is gone. The potential energy of a spring at the breaking point would be different than the original spring. So I guess I could rephrase the question, what happens until that point? Does it get let go as heat?
Fair enough, thinking about it at a microscopic level, individual molecules/atoms of material will be pushed into positions where they are being repelled from other atoms/molecules via electromagnetic forces. Those forces won't go away as the chemical reactions happen; so, I would guess that the answer is kinda the same as it is at the macroscopic level. When the bond which holds an individual atom in the lattice of the material is broken, those electromagnetic forces would push the resulting molecule away. So ya, it becomes heat.