Some thermostats run off of the power provided by the main equipment and some run from batteries. Some of the former have back-up batteries to hold their programming in the case of power failure.

If the cover is removed, you should be able to see a printed model number. One you have that you may be able to search for the owner's manual. You can also call Honeywell for help.

What problems are seeing with the thermostat?

Your t-stat probably needs replacing figuring as though it doesn't have any batteries and is not functioning or your unit itself may have lost power. Time to call Joe the ac guy.