Yeah this is often indicative of a problem with the charging port. I would try another factory reset as Paul suggested. Also, shut the phone down and pull the battery. Let it sit out a minute or two then put it back in and power up. Then charge to full and see if it continues. If it does, you may want to try lightly brushing the charging port with a toothbrush and a little bit of high % isopropyl alcohol. But I would try spraying out the port with a can of compressed air first.
Hopefully your phone doesn't have light water damage, which I've heard about affecting the port on this phone. If all else fails, you should consider taking it into a Sprint tech center and have them look at it.
Good luck!