iPhone 3G can't be charged full.

when the battery charges it gives an initial high burst then the final part is a trickle charge. So if the battery is getting old (as yours will be) then it will have trouble charging and running all the background work like antenna reception, push notices, GPS etc. You may find that if you turn your phone to airplane when you charge it that the drain isn't so noticeable. Basically the functions are more of a drain than the charging process can meet when it gets to the trickle charge...

Change the battery, if that doesn't solve the problem then it may be the dock connector (try cleaning the port with a toothpick to remove any pocket lint that may have built up)