If one uses Jlime then there is no reason to have the backup battery in there. Because every time one restarts Jlime the internal memory is completely wiped
. And the backup battery is only there to preserve the internal memory (if the regular battery should run out of power or if one replaces it). That way WinCE can take off where it left (see Kristoffer's explanation).
The backup battery is only
there for WindowsCE. If you use both WinCE and Jlime then the backup battery is useless
. Because every time you switch from WinCE to Jlime the internal memory is wiped.
I'm afraid you should remove the backup battery as long as you use another ooperating system next to Jlime.
[semi off topic]
Is there one particular application you still use WinCE for? It may not be necessary for you to use WinCE. See for instance my entries in the Jlime homepage Wiki
on all the things I use my Jornada for. Chances are you do not need to reboot into WinCE anymore.