I don't know if it's a glitch or intended, but I lost a shiny landorus in the safari zone shiny breeding programme. I left a shiny landorus sitting in the safari zone for a few days worth of runs, as I was waiting to level up my main partner before catching it, and when I went to the the safari zone just now, it was no longer in the programme.
I'm not sure exactly how many hours or runs I did since catching it in the ADVENTURE, but I checked the programme periodically and it was there for a number of runs. Maybe it got shoved out by newer shinies? Just in case I had been catching the other shinies from the ADVENTURE to make sure there wasn't a limit or something, but maybe there's an internal counter and it got overwritten by newer shinies?