In a synth with patch memory, if the memory consists of a volatile type of RAM, it is necessary to maintain power to the memory at all times to avoid losing the patch data. In these types of synths, a backup battery maintains power to the RAM when the synth is powered off. On many synths, there is no specific indication of when the backup battery needs changing; the first indication is when the synth "forgets" patches, or begins to behave oddly.
Usual practice in the industry has been to use long-lasting lithium batteries for this purpose, although a few 1980s synths used nickel-cadmium batteries. These had an unfortunate habit of leaking and damaging the circuit boards they were mounted to; the Korg Polysix is notorious for having this problem. New designs are tending toward using flash memory or some other form of non-volatile storage, so that a backup battery is not needed.