So, wait, should we run it down or let it charge? I'm so confused.... (Aren't most batteries lithium-based now?)

At least I'm not the only one - a few years ago I bought a Scooba robot to clean my kitchen floor, and the battery would always die before it finished. The manual said to leave it plugged in (theoretically, charging) all the time - which I'd always thought was bad. Eventually I looked up troubleshooting info on their website, and their advice there was to charge it only when you were going to use it! (I did get a new battery under warranty, but I've just replaced that one too.)