said by icorbin :
So it is OK to pump air into the well side of the check valve to see if it is holding pressure? That's not going to force water back down the well? Or will the water in the bottom of the well pipe act as a cap or resistance on that end?
There should be a check valve at the bottom of the well -- that is what this test will check. My guess is that the lower check valve (may be called a foot valve) is malfunctioning.
[edit] As far as the well having to be re-primed, it depends on the depth of your well. A shallow well will pull it's own prime, a deep one will not.