If you were to decide to replace the batteries in a ProMark 3 (or MobileMapper CX) yourself, a good source of replacement batteries would be:
https://www.digikey.com/product-detail/en/elna-america/DSK-3R3H224U-HL/604-1020-1-ND/970232
The part is actually a 220 mF super cap. (That is milli-F, not micro-F!)
They are less than a buck-fifty each.