I have a 2006 JD 3320 hydro.
After about a year and a half my John Deere battery just up and died one day, luckily while I was in the back yard. I shut it off to grab some lunch and when I returned it would not crank, no prior warning signs. When I went to remove the battery I noticed that it had bubbled over and corroded the battery tray and everything in the area. Maybe this was happening over a period of time as I don't recall specifically checking the battery because there were no problems starting (my fault for not checking sooner). I wanted to replace with original equipment so I got a brand new JD replacement, same model. I watched this closely and in no time it started to do the same thing. I took it back to the JD dealer and got my money back, bought a non-JD brand replacement and have little trouble with this one.
This tractor has been awesome otherwise; I blame the battery design, not the tractor.