S5500 loses time and seeting when battery is changed

If the laptop battery is more than 3 - 4 years old then the battery could be worn out. Rechargeable batteries have a finite number of charge and discharge cycles and will lose their charge capacity over time, i.e. won't charge to 100% and gradually the charge reduces until the battery won't charge up at all. OR The battery shows a 100% charge but when the adapter is disconnected the battery drops off to zero capacity in a very short time. If the battery drops to an unacceptable charge level then the battery needs to be replaced. Rechargeable batteries will fail if stored in a discharged state for long periods.

Maybe you need to change you're laptop battery, baterrys by usage lose battery life

Sounds like it might be time to change the batteries. Even if batteries are charged correctly they eventually lose power with use and need to be changed. Here is a link to the battery needed for the Jazzy 1103 Ultra http://www.replacementupsbattery.com/UB12350-NB.html

Theres a small back-up battery located on the main
power board. It's not a DIY project to replace this battery.

Hard to say exactly with out checking myself;

Wrong (to low amps) battery, poor condition of battery clamps, loose cables going from battery to starter assembly, battery installed in reverse polarity. Perhaps the NEW battery need to be charged ( storing a battery on concrete (cement) slab will cause a drainage of the battery and it doesnt take long)

I don't have any experience with a fuji but I do believe it has a small internal battery that keeps just enough juice to operate things like date and time. I would take it to your local camera shop they will stear you in the right direction if not make the repair for you.

Rmove the baterry and start without baterry, and put back the bateryy after restart . 

This gona sound ignorant and obvious but you have a short in the abs sys or ECM -----get a code reader from Advance auto to see if you can pinpoint the issue----you give them a deposit then when you return code reader they refund your deposit---oh have you changed anything in the vehicle such as radio----added speakers---had an accident--new ign sys etc etc---GL

I had the same problem, the best solution that I found, was to make sure that I put the new batteries in with 30 secs, and the date etc, remained at the correct time.