It took me three days for my breebly. It's completely random, but yes, it will go on a retired petpet, and no, I don't believe a pet can 'reject' a petpetpet. I have found, however, that it goes faster if you only have that page open, and if you manually refresh, rather than using the F5 button. My breebly took 3 days, my cooty about 2 hours, and my mootix within about 15 minutes. Kepp trying, it'll attach eventually.