It certainly would be a punishment. Or if theology is to be believed, is a punishment. One of the most terrifying moments of my life was realizing the universe may be eternal. In that case it has always existed, and always will. Moreover, it never had the option not to exist. It exists independently of any desire to. That made by blood run cold. At least mortals have an end to look forward to...unless theology is to be believed.
Even heaven would be hell if it never ended.