The power doesn't say anything about not being able to heal once this power is revealed and they don't have a second starting line, nor does it say they can't be healed past a certain line. But since when they land on these special powers, the intent it to become a single character, just double-checking:

Can you heal them or Cable/Deadpool regenerate back to their Duo clicks?

You can heal them back up. They will get the attack symbol again (since the power that gives them the attack symbol is gone). When you eventually click back to the power, you will have the same choice you made the first time.

Cool, thanks.

You get to make the choice again? I would think you were forced into keeping the same choice you made since it says "once per game."

You are correct. Sorry if that wasn't clear. You are stuck with the same choice you made the first time.