I don't think you can draw any conclusions from the assumption that the soul exists, and I'd have to argue along the lines of theological noncognitivism. I don't think you've given us enough information about what the "soul" is, what states it can / cannot exist in, for me to even consider the question of whether it can be eternal as valid.
To me, it's like asking "Assume X exists (where X is a new flavour of ice-cream). Is X tasty?"
I have absolutely no reason to even attempt an answer to that question, given that I've got nothing to go on. All you've told me is that we are assuming the flavour exists; whether my taste-buds would respond well to it can't be answered with that assumption. Likewise with your question; I've got absolutely nothing to go on when you ask whether this assumed "soul" would be eternal or not.
To me, it's like asking "Assume X exists (where X is a new flavour of ice-cream). Is X tasty?"
I have absolutely no reason to even attempt an answer to that question, given that I've got nothing to go on. All you've told me is that we are assuming the flavour exists; whether my taste-buds would respond well to it can't be answered with that assumption. Likewise with your question; I've got absolutely nothing to go on when you ask whether this assumed "soul" would be eternal or not.