You didn't say which synth. Most of the old ones I am familiar with had a battery that provided power for retaining the patches after a power off. This was in the days before flash memory was in wide use, so if the battery died the patches were lost too and had to be reprogrammed.
I just had a battery replaced in a Yamaha DX 7 II a couple years ago. It was soldered in. It had the same symptoms that you describe, the patch programming would be lost after a power off, until the battery was replaced. I will have to give my respects to the maker of the STeem emulator. All of my patches were stored in DX Android format, an old Atari ST patch librarian. The STeem emulator ran the program perfectly, even down to using my PC MIDI ports to transfer the patches back to the DX.