I submitted this to “Ask This Old House”.
I installed a propane on-demand hot water heater. We use a small tank (think BBQ size) which we swap out periodically. The unit itself is outside but does require electricty for the control board and to operate the igniter and valve.
When installing it, I realized that we can lose power anytime even without storms (think car accidents along the only road). In the room just the other side of the heater I have a big screen TV which is on a UPS (Uninterruptable Power Supply). It gets its power from the wall outlet and charges an internal battery. If the power goes off, it can still supply power to attached devices until the battery runs down. I ran a power line from the UPS to power the heater since the elctronics draw very little. This is not unlike you car where the engine charges a battery and even if the engine is not running, you can still listen to the radio (for a while).
Without the UPS, if the power went off, the hot water would stop instantly even though there was propane, because the controller would be off. This way, if there is a power failure during a shower, there was still hot water to finish. It would not help if we were using the washing machine or dish washer because they draw too much power for the UPS to handle.
The UPS I use is about $100 from Costco and is always online for the TV and water heater. It also has built in power conditioning against surges, sags and spikes.