I know that Gauntlet I saved the last level in RAM only. The information was definetly lost when the power was shut off. I am almost sure that gauntlet II works the same way.(posted 9443 days ago)It is very easy to add code to MAME to let the user select the level on startup (for both gauntlet I and II) and save it in the inp file. I even submitted such code to the MAME team about 18 months ago but they did not like the idea.
For my own use I then patched the Gauntlet I ROMS to save the last level in the EEPROM instead. I planned to do the same for Gauntlet II but I never got the time to do it.