Apologies if this is a repost but I attempted to search for this but couldn't come across anything.
Anyway I stumbled across this earlier today as I was doing the Thundering Pandaren Spirit daily. My LFR queue came up as I was on his last pet and just as I finished the battle I accepted the queue. After completing the LFR I left the instance and was able to verse him again.
I then tested this theory on another of the spirit tamers by entering a random BG queue as I got onto the last pet and accepting the queue just as I won the battle. I left the BG and again was able to verse the tamer once again.
The advantage of this is for those that are able to solo/duo these tamers with a carry pet in, you can get the pet xp multiple times. When I found this on the Thundering Pandaren Spirit I was levelling a pet with two other pets and both times I defeated him the pet I was levelling received experience and went from level 20 to level 22 in the first battle, and then level 22 to level 23 (close to 24) after the second.
It may be better to use Pet Battle queues (if they work, not yet tested but will test after dailies reset) as there is no repercussions for forfeiting like there is for leaving a BG or dungeon.
EDIT: Can't queue for a Pet Battle while a battle is in progress. So this method will only get you two battles unless you wish to participate in whatever queue you use to avoid the debuff.