Funny, I thought the internal battery time on wifi was much less than 3 hours and had to recheck my own post! Anyway, here I've mainly been externally powering mine from a little box which holds 4 x AA rechargeables and which has a USB socket putting out presumably 5 or 6 volts. As I recall it, when I powered the recorder from a rechargeable power supply offering multiple output voltages, 5 volts didn't work well but 6 was fine. Personally I have no big problem with having the recorder on a stand and the battery on a longish USB lead at the base of the stand - that wire is no issue compared with a mic wire going back to a distant recorder. With such an external supply and with fresh batteries in the recorder itself (just in case) you'd be able to forget any worries about losing power. The phone display tells you whether it's on external or internal power for your reassurance, and shows how much internal is left on a simple 3 (?) bar display. But when you're down to one bar, wifi might shut down at any time.
Afterthought - perhaps there should be a menu option to allow you to set the device to start recording automatically if wifi is turned off by the device, thus covering the situation that you were stopped or paused when the link was lost, and you can't restart the recorder to capture the rest of the show. After 3+ hours, you should have your levels correct so really you don't need the link so much.