I did some more searching, lipo batteries in this voltage are usually labelled as "3.7V" meaning they are a cell with protection pcb that operates up to 4.2v (full charge) down to 3.2V (discharged).

The battery cell in mine measure approx 12mm x 18mm x 2.5mm (WxHxT); with the proection pcb it was a total of about 12mm x 22mm x 2.5mm.

I ahve not found an exact replacement, but did find 10mm x 20mm x 2.5mm cells which should fit... going to order some and see if a bit of soldering will ahve a better running fitbit. :)

The band on mine fell apart but I already had one sent for warranty. Min still worked so I took it apart, and while trying to look for a replacement lipo (Searching the number on the battery) i came here... The batter is measuring between 4.1 and 4.2v. There appears to be some sort of protection or charging board taped to the lipo that I think we need to keep if we are to replace the lipo battery.