My Payne heat pump was installed August 2003. Noticed a few months ago that it would run constantly. Had it checked out. Repairman said it was leaking through the flare fitting. My question is: If a flare fitting was tighten three years ago can it jiggle loose on its own, because of the vibration when it runs?

Normally a Flare fitting is as good as the flare it is made up of. Usually you have to use a special flaring tool to make up the flare. Where some people mess up is when the fitting is large like a 5/8 or 3/4 or 7/8 they forget to put oil on the male part of the flare threads. Without the oil the flare is harder to tighten down to make a good seal and can eventually back of just enough for a small leak.

Vibration can also cause a leak especially if no oil is used during assemble.
If the fitting flare assembly is cocked or put under stress just a bit during assembly that can also cause a problem.

I prefer to braze my refrigerant connections but there are a few companies that use a flare. One nice thing about a flare is the you do not take the chance of burning up the valves at the condensing unit while brazing.