setInterval not working after save()?

It sounds like you're doing everything fine. Do you get any error messages when you load()?

I guess you could try initialising the LCD and DS3231 after a delay in case that's a issue? Maybe the DS3231 takes a while to work after power is applied - if you got the wrong time out of it then maybe setTime sets the time to something invalid and that breaks the timeouts?

You could try running dump() to see if any intervals/timeouts are actually set up to run, and maybe check getTime() or new Date() to see if the time is what you expect it should be.

Finally, it's unlikely I ever checked what happens if you reset the time to something else and then immediately create intervals, so I guess you could try setting the time inside a timeout?