PPCGeeks - Confused about charging the TP

Usually phone charging is very simple and predictable. You plug the phone on the charger, the phone charges in a few hours and keeps on AC power after it is completely charged. Battery capacity is relatively similar, the battery gauge is accurate. However, the TP is different..

1) When I keep my phone on and charge it through the night, it is still charging in the morning after 7-8 hours, the LED lights in charge mode. At one point it has finished charging, but for some reason it seems to default to battery usage once fully charged. This results in battery drain, thus causing the charging to begin once again. Why doesn't it just use AC power?? This can't be all that great for the battery.

2) If I try to keep the phone off and charge, the LED lights are solid, battery is fully charged by the morning. However, when I use the phone, the battery drains quicker than it would if I charged it using the first method.

I'm on my second TP right now, with the same issue. My Mogul never had this problem, and I'm just baffled and don't understand why the heck it's so hard to charge this phone properly.