This isn't necessarily worrisome. 3C Battery Monitor has several options when it comes to how it records current flow. If set wrong, you could get something like this, or even show charging current when unplugged and vice versa. That can be set during the initial setup, or in the settings for battery monitoring. It's one of the more powerful monitoring tools, but not the most user friendly.
I'm with B. Diddy, though, that it's likely a battery and phone age issue. A dendrite is a growth inside the battery that can cause an internal short, which explains the lack of charge when turned back on. They can become prevalent on older batteries. It acts like a fuse, in that it is destroyed when it shorts out, but can grow back. With this being such an old phone, the chances of finding good batteries is slim to none. All batteries wear out from age even if just sitting on a warehouse shelf, and no one is making new batteries for this phone anymore. You could try buying more batteries, but I feel it'll be wasted money.
Given the relatively ancient specs of the phone, I think your only long term solution is to buy a newer phone.