If the computer goes down or battery goes dead? I don't remember if there is a specific rule about that or not, to be honest. But I just have to use common sense on this one. I would likely ascend, do a slightly longer safety stop, and surface to swap out the console. That's assuming you KNOW you have not exceeded your NDL. I guess if you HAVE lost track of your NDL by a very significant amount it might not be a bad idea to stay out of the water for 24 hours.
"What ifs" like this one, in my opinion, are good reasons to know how to use dive tables, and to wear a dive watch as backup. Remember, no matter what the certifying agencies want you to believe, it's not impossible to dive without a computer and there are still a lot of people out there that do it, LOL.
Anyway... good luck... I think you will really enjoy this product. I know I am very impressed, especially with how customizable it is.