I just started doing these quests but now it is telling me, None of your pets are eligible for battle. Did they stop them temporarily?

They're still going. More then likely, though, you have a pet stuck in battle. pokes third link in siggy for guide on how to unstick it

I finished the quest . It tells me all my pets are not eligible.

Yeah, none of your pets are eligible, so you can't battle. It's not the BQ's, it your pets (I'm doing BQ's right now myself). There could be several reasons that has happened, your pet somehow got left in a battle, or is hungry, or got really stuck and you need to file a ticket.

I will check it thank you.

Just so you know, there seems to be a glitch going around with the resort not feeding your pets, so definitely check the hunger bar if you have them lodged in there.

Thank you. I put them all in there and it was fine for one quest. I will try feed Faded it was that thanks for you help. I sure hope they fix it soon