It sounds like insufficient flux. You can't simply reheat, but you shouldn't need to cut.
Just unsolder, reflux, and reflow. You gotta blow the old solder off, though, before you can refit. Else, flux them good, them slip them together hot, before flowing additional solder.
Cutting and refitting only works if you still have enough slack in the pipe left, and still, you may wind up with a "cold" joint, due to inadequate preparation/insufficient flux...