I bought a 300 watt power inverter for a long car trip. Plugging in the iPhone 4 yielded inconsistent results when trying to login. My wife was complaining she couldn't login sporadically when the phone was charging. Unplug the charging cable, no issue; plug the charging cable in; sporadic login issues. The cheap power inverters don't generate a true sine wave A/C; maybe the phone is sensitive to that.
So what I'm thinking, is that there may be an issue with your power at the source, you may want to have an electrician come in and test the lines. You may not have clean power and not know it.
Most power inverters a consumer can buy do not produce a pure sine wave like a wall outlet. They produce a square wave which have have an infinite number of harmonics and will have an effect on some electronic equipment operations. On a project at work I needed to replace gas generators with battery power. I bought pure sine wave inverters for about $2500 each. This was due to the required power consumption, about 2000 watts continuous and the equipment I was running would not work accurately with any other power except DC which was not an option.
In another case I tried to use a 300 watt power inverter I bought from Pep Boys and the device I was trying to operate failed continuously, it would start to power up then would fail. It only drew about 20 watts so I knew it wasn't the inverter overloading.
You can check your outlets, whether they are wired correctly, real easy. You can buy an outlet checker at Home Depot,
https://forums.imore.com/e?link=htt...%253FNao%253D48%23.Up5SpdtXskc&token=v3LNSvht
I have both a GCFI and a non-GCFI type I use when there is any chance of incorrect electrical wiring. That may shed some light on the problem.