Never had this happen before. My backpack was full, so to make room I decided to put some of my pets down. I put them in the fenced area of my red barn farm. I tried to pick them back up a few days ago but couldn't. I logged out and back in, tried picking them up again, and it appeared that I was (with them disappearing when I did) but then they were not in my backpack. I walked into my house and back out and there they were, right back in the fence area. I then tried to pick them up using the move furniture button, but couldn't budge them.
I sent a bug report to KI, but haven't heard a thing back. The problem is that these are some of my really good pets and I need them! Figured if KI isn't gonna answer me, maybe someone here has experience that could help me.
