We don't know much information but some people found out that it actually isn't to do with Neopets itself but rather the CND company they use. All we can do for now is sit tight as it appears to be out of Neopets' hands too.
Head to the Grundos Warehouse to enter the code YOOYUAUGUST for this months prize - a Green Yooyu!
NOTE: This code is only active for the next 48 hours so act fast!
For more information about August's Altador Cup Edition AMA, you can watch it on their official youtube page featured here.
Did you try healing your pet? It might be that the game thinks you're still in the battle. Or you could see if you could end the battle by withdrawing here: https://www.neopets.com/dome/status.phtml
If that doesn't work and you can't start a new battle when your pet is healthy (or with another healthy pet) I'd suggest to sent in a ticket to TNT.