OK - the typical heated CPAP device will consume 100 watts per hour if heated. I am going for the extreme case for safety.

a) Assume you will use it 8 hours per day, for three days.
b) Assume a 10% self-discharge rate for (3.3% per day).
c) Assume that you will want 200% of necessary capacity - that is, discharge the back-up device to no lower than 50% to avoid damage to the batteries.

3 x 8 x 100 x 2 = 4,800 watts.

Allowing for losses, and self-discharge as-noted. You will need a device capable of supplying 48 amp-hours at 120 VAC.

Without redundancy (dangerous). your typical 1500 watt UPS will operate at roughly 3 hours per 100 watts, without damage, and run in the $500 - $700 range.
You will need eight (8) of them to meet your most basic need. And have to change them twice (2x) per night. Or, you could spend $3,500 for a single unit that could run for all of eight hours at 100watts.

Get a generator. Be wise in your fuel selection. You will have four (4) choices:
a) Gasoline: Gasoline generators are amongst the cheapest of options, and even a relatively small one will run all critical functions in the typical household including your refrigerator, some lights and the CPAP. It will burn something on the order of 1.3 gallons of fuel per hour. So, you will need to store 30+ gallons of fuel on-site, and fill it as needed. At night. Or 94 gallons and run it 24/7. Gasoline devices tend to be either large, powerful and noisy, or small, quiet and low power. Anywhere from $400 - $1,000 will get you there. No transfer switch, strictly a manual device.
c) Diesel fuel: This would be a whole house device, and if installed with the proper transfer switch, and with a large tank, you could get up to a week with such a device. But they are not cheap. You would start around $1,500 without installation or a transfer-switch. So, figure $3,500 absolute minimum installed. And that would be for a Chinese-origin device. A decent Kohler device would be about $4,500 installed.
d) Natural gas: If you have a reliable source of natural gas - about the same installed cost as a diesel - and no fuel limits. By far, the cleanest, lowest maintenance option, and least expensive to operate.
e) Propane: As above, but you would need a large propane tank with the associated issues.

The issue with medical devices is that one does not want to screw around with 'good enough' - as that 3-day issue might turn into a 4 or 8 day issue.

Peter Wieck
Melrose Park, PA