Power outages are infrequent where I live these days, but it happens enough that it freaks out some of my gizmos. Most of the time they are momentary power blips of a few seconds, but enough to turn off/on and screw things up.
So, I decided to put in and use a couple of small (and not too expensive) UPS devices to prevent power loss in some cases. Not much can help an hour, day (or longer) outage, but these devices save the day for the occasional blip. The ones I got were around $40 each, and can keep a small gizmo powered for 15-20 mins to prevent an off/on condition when power fluctuates once, or a few times briefly. So, get one for your Echo to be plugged into.