The RAP5 should preserve configuration between power down:up events. I have run RAP-5's on battery packs many times and thus the power comes and goes as I switch on-off the battery pack.
When you say factory default, the embedded WEBUI asks you for the Master controller IP address again?
I have noticed this on occasion as well (both with 2WG and 5WN). After either a power blip or Internet outage a small number of RAPs lose what seems to be their master hostname. They do not connect to the controller, nor do they display provisioning page when connected via wire.
There is a bug in 5.x that is fixed in 220.127.116.11 that should address this issue. The issue is that the RAPs will lose their configuration after a WAN outage or reboot. If you open a TAC case, the can give you more details. The bug is #53443.
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