some swithcmode powersupplies do not like sinewave inverters. its why thse days theres been a big increase in 12v-laptop adaptors. my 600w sinewave inverter wont fire up my toshibas 240v adaptor but will quite happily run my old desktop pc, monitor, speaker amps, modem and the hub.

not knowing what the hell a CPAP is or whats inside it I'll follow the guess of excessive line loss from the battery to the inverter causing it to drop out.

If you want a hand with it let me know as I might shortly have a trip out towards bribie coming out to have a look at a certain website founders gearbox issue and to get one of my workshop manuals back.