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?

I'm not too sure you're correct regarding the UPS not being ok for the 4w. devices. I assumed it depleted what was drawn. I use an old UPS to power my router and phone and it worked fine for a 2day outage.

That's good to know! Do you recall the model and/or size of your UPS? I may need to look for that one.

I've got an APC SUA1000 for my computer. It's a 670 Watt 1000 VA UPS.

They provide a web page for estimating runtime, at SUA1000 Features. It says the min-max range is 67-670W. When I put in 4W, it says, "The total load (power draw) entered is less than the minimum value for this product (67 W)." Not sure exactly what that means; will it not work, or is it just that they don't recommend it?

I also looked at the Jackery Explorer 160 Portable Power Station (which looks pretty nice!), but it automatically powers off after 6 hours if drawing less than 10W.

So it appears the behavior depends a lot on the particular model.

Correction: my ISP's 24 hour solution DOES use rechargables. (It looked similar to a different model that takes D cells. I got confused.)

It costs $300 and is single-purpose for the VoIP connection box only.

We kept a back-up copper line for about 5 years. In the end we decided that our cell phones were fine since 90% of calls go through them anyway. If cell service is unavailable, my UPS seems to work fine for the sorts of minimal power outages we get here. Don't see why a low draw wouldn't last about what calcs would show given the battery size you work with, the UPS only sees the draw and that is normally pretty linear effect on the battery.

The battery itself might be linear, but the UPS isn't - not at low power levels. The UPS itself uses power - I've seen numbers of about 10 watts for a 1000VA UPS. So if your load is 5W, then runtime calculations will be off by a factor of three (since the battery needs to supply 15W, not 5W). There may be other effects in either direction that I don't know about yet.

I just unplugged everything from my APC SUA1000, plugged in a 4W nightlight, and pulled the power plug. It stayed on, for 3 minutes at least. Yay.

However there are plenty of reports of other makes and models that DON'T work at low power levels, in addition to some reports that representatives of APC itself said, "their UPS won't function properly with such a low load."

There are lots of people claiming, with great confidence, exactly opposite opinions about this topic ( UPS for tiny load , How To Disable UPS Auto Turnoff? , etc.)

Unless you're the engineer that designed the thing, I think a few experiments on actual devices is worth any number of guesses.

The UPS's inverter will draw some power like you said. Your other option is to fix up a low voltage UPS. For example my router takes 12v in from a little 12v 1A transformer. So its pretty easy to run from a 12v SLA battery eliminating the inverter loss of an off the shelf ups.

USB powerbank with pass through charging?

It's not an uninterruptible power supply as likely drop for a fraction of second switching between input power and battery.

This seem sufficiently answered, but a few thoughts.

First, internet and VOIP are immediately backed up by UPS at my house. These tend to last several hours for me. You might plug your 8 hours backed up device into a UPS and stretch it to near the 24 hours you want.

Second, you can buy rechargeable D cells. So you could buy the 24 hour backup system and periodically top up the D cells. In fact, you could store more D cells and make it last even longer.

This is all pointless if the equipment on the other end of the line is down. That's what tends to happen where I live. Everything (cable and cell systems) has backup power for a few hours but eventually fails. Most service provider sites are rigged for generators but don't have one onsite, so unless one is brought in, the system stays down. Last time we lost power my cable modem was blinking but there was no one on the other end.

To complete my answer your actual question, I have a generator that recharges the UPS(es) and I can keep things going for a few days if needed. For a while I had starlink internet, which would in theory stay up during an outage. I switched back to cable, unfortunately.

Final comment, I'm getting solar and batteries. With that the house should be able to run quite a while w/o grid power.

I once played my digital piano for several hours on a 450 watt (?) UPS during a blackout. That was with headphones, not the speakers. So a UPS can indeed last a long time powering a low wattage device.

But rather than trying to provide backup power for VOIP, I'd just go for a cellphone. And have a separate rechargeable power bank. And use text messages rather than voice calls. For one, text messages take a lot less power. And second, they spool up at your ISP if they can't be delivered immediately (say if you only want to only turn your cellphone on for five minutes at the top of every hour to save even more power). If the power outage takes down your cell service ISP this won't work. But in that case, any VOIP provider you have would probably be down as well.