I'm finally getting pushed off my copper phone line to fiber/VoIP.

Grump, grump.

The faster internet will be nice, I suppose, but I'm unhappy with the available power backup options for keeping a phone going during a power failure.

My provider offers for sale an 8-hour backup device with a rechargeable battery and a 24 hour one that runs on a big pile of non-rechargeable D cells.

8 hours isn't really long enough. We've had power failures of about that length within recent years.

The usual computer Uninterruptible Power Supplies are not designed to keep a low power device (e.g. 4 watts) going for a long time - they're designed to supply a goodly amount of power for keeping your computer going long enough to shut down cleanly. You can't just assume that if you draw 1/10th the power of your computer that the UPS will run for 10 times as long; I'm not sure it's linear like that at low levels.

I'd like a 24 hour backup that uses a rechargeable battery. (Reliability would be nice, too.) If I can't find one, I may have to build my own.

Do you have a solution that you like?