Contact L6 Technical Support and set up an issue ticket with them. My first charger that came with my JTV59 in 2011 acted like yours and they replaced it when I contacted them. The 2nd unit works fine. I purchased a 2nd JTV (a 69S) last October, and the charger that came with that one was fine. There's really nothing that can be "fixed" on the charger. Was this your first time using it? My first unit didn't work right out of the box. I also power mine with the pedal (an X3L then, and now an HD500), so I rarely use it on battery, but do keep a charged up battery on hand, just in case I have problems with the VDI cable (had it happen -- must have stepped on the VDI connector).
As a result of opening the ticket, LIne6 sent a replacement battery which worked perfectly in the existing charger and in the guitar.
All is well with the world and I still love my JTV-89.