My wife has a small lithium battery for her CPAP when we are dry camping for some time. We used it when we went to Alaska. It will run her machine for over 2 nights with out the humidifier. When we traveled she just plugged it into the inverter plug in the truck (this when we had our Truck Camper the Ford had a 400 Watt inverter in it). After a days travel the battery was fully charged.
Now with our Super C we have 4 6volt AGM batteries and 480 watts of solar. So between traveling and the solar and bigger batteries their is no problem running her CPAP anytime. Our generator also has a smart controller that can be programmed that if the batteries get down to a set level (decided by me) it starts up and charges the batteries automatically. It can also be set to not come on certain times of the day or mainly night. So at this time I think we have her pretty setup with her CPAP and don't have to worry about hers not working. The controller also is smart enough that if it notices coming up to a quiet time and the batteries are down it well start the generator up for 2 hours in advance of this time to give them some charge.