They have battery for extended run, don't they? At least enough to get you through the blips?
--Patrick
No. If your power is unreliable they recommend a UPS, but they also have battery packs you can buy if you don't mind spending a whole lot of money. Some users build their own backup systems because the UPSs typically beep loudly and wake them anyway.
I've got a small 12v battery and inverter for power outages to run mine, though due to power consumption I leave out the humidifier if I'm using it.
But the waking up when it turns off is pretty startling, because you are usually a little disoriented and can't immediately understand why you feel like you're suffocating.
You aren't, though, the masks always have venting so you have access to fresh air, but it's still limited, and you do still end up rebreathing some of your previous exhale through the tubing, so the CO2 concentration still increases and your brain sends the adrenaline surge to demand air with lower CO2.
Your body doesn't actually measure oxygen level, it wants to see low CO2 levels. This is one reason why CO poisoning is so bad, it prevents oxygen absorption, but since the CO2 level never increases you don't realize you are suffocating, you just get sleepy.
Sooooo.... anyway, long roundabout answer for "no, these expensive medical devices do not contain any power backup capability."