My Epic was experiencing the same issue. When I first got it today, it was gradually charging fine via my new Thinkpad's USB port. But then for some reason, "Battery Indicator" showed the charge going down, even though the red LED and the battery icon indicated that the phone was being charged. So did my lock-pattern screen. I called my local store for a replacement.
The phone wouldn't charge while I had the rubberized phone cover on, bought from the Sprint store. Also, the phone felt very warm, so I took the cover off, opened the battery cover to see how hot the battery was. It didn't feel too hot to the touch. I removed the battery, put it back in, powered the phone back on, and saw a huge green battery charge icon, but alternating with an icon with what I think was a yellow warning sign, and a thermometer on it. So I left the Sprint rubberized phone cover off, and recycled the power on the phone.
After the phone fully loaded up, I tried USB-charging the phone. Now, it's gradually charging up (was down to 14%, now back up to 19%). The phone feels cooler, too.
I'm leaving the replacement option on the table in case my phone turns for the worst. I rely on the phone for work and business so can't be without a phone. Maybe I should reconsider getting a land-line or VOIP service again. But maybe, this being a brand-new phone, the battery needs to be cycled a few times before it stops acting unusually. I'll try the wall charger before I head to bed tonight, and see what happens tomorrow.