That is sort of a loaded question.
If you mean when u log at home will u lose your pet? The answer is now. Like the previous person said it auto logs with you even if you have a full stable.
however if you mean will my 2 pets that i have "blue" training magic, eval, med, and resist in the safety of my house be there in the morning when i get up...
i have seen this go both ways. I once let a couple of bakes pound each other while i was at work. 10 hours later still there no problems.
a different time i had a mare and unicorn go at it. Ran to mcdonalds for some lunch, 30 minutes max. Unicorn dead and mare wild when i got back. Both were wonderfully happy when i started.
if your pets are crazy high resists. Dont risk it! That unicorn was 3 points short of max resists. 200 + tamed uni's later. Not one even close to the one i lost. It only takes one screw up to stop "blue" training while your not attended to never do it again.