From the way you are describing this issue it does sound like it is internal. Do you recall any time when your phone was charging and it fell, sat on by accident, or anything else that could have bent/put pressure between the charging port of the phone and the connector? If the battery had an issue the phone “would” tell you. I still have my Droid Incredible by HTC which I am sure is not any much different to the second version. This sounds like you need to have your phone checked and serviced at a local VZ store.
It's the loose charging port. These phones are known for it. They'll replace it, but your phone has to be PERFECT otherwise.. any scratches or cracks, and you run the risk of them saying you dropped it, and it's your fault. Once you get a replacement and ship yours in, you risk them charging you full price for a new phone.
I'm on my second Incredible 2 with the same problem.. sometimes it catches and charges, sometiems it doesn't. I got an outside battery charger and some extra batteries, and just replace it during the day... It's very frustrating but the phone is so great otherwise, that I opted to get a second one (after my first 'broken' one fell into the subway tracks, paid the $100 for a replacement through the insurance).
If anyone's had better luck getting it replaced for free, I wanna hear it, because I'm up for new every 2. This is the ONLY problem I have and willing to hold on a little longer to be sure kinks are worked out on the new batch of phones.