Expression for when you've fixed something, but something else breaks? And repeatedly?

The software industry term of art for the basic fix-causes-breakage phenomenon is regression. Hence the derived term regression testing, in which one is testing whether any fixes one made broke something else.

The ongoing chain isn't commonly discussed, but cascade regression immediately comes to mind to describe it.

Within software development community I agree that regression is the best term, but informally I've heard people call this "whack-a-mole", after the carnival game where "moles" quickly pop out of holes and you have to hit them before they vanish. I am not sure why people use that term, since it doesn't capture the causation, unless it's because you just keep pounding away, with no way to predict where the next mole (or bug) will arise, hoping that you can be quick enough to catch each.