i've only ever gotten bored w/ my tama once--it was a v1 and i was just... ugh. it seemed like it was being really repetitive and i was getting sick of it. so i put it in a big box where it wouldn't get hurt and i'd always be able to find it, left it for a while (about 2 months), and when i came back for it, i was NOT bored anymore.
also, some things you could do if you're getting sick of your tama:
-kill as many as possible. my friend did this, then she got back into tamas after a few weeks of killing them all.
-try to get the worst characters/best characters, then overfeed them, play games nonstop... if you're still sick of it, i dunno... you're crazy.