We have a double line jet pump for a deep well. It keeps cycling on and off every couple of minutes. We suspect that the foot valve is gone in the well. A couple of months ago we changed the water tank and that seem to remedy the problem for a while, but it is back doing the same thing. The ground is still frozen here so before I dig up the well I am wondering if a put a check valve on the intake line would that solve the problem at least temporarily?

Not a Well Expert for sure but I think if you have a new tank and if you can see the pressure gauge slowly drop down then that is your problem. Makes good sense to put a valve on the intake line until you can get to the foot valve in the spring. Just food for thought but if your foot valve is bad, it could get bad enough that you would not have a prime, I would think. Wait for the pro's to come along.

You can put a CV on the suction line. If it works, and it likely will, you won't need to replace the footvalve. That would also prevent the pump from losing prime. The closer you can put the CV to the wellhead, the better. The nice thing is this: not much cost, and not much trouble to at least try it.

I am assuming, BTW, that you mean it is short-cycling while water is not being used. That points to either a footvalve problem or leaking wellpipe.

I do find it a little odd that replacing the tank seemed to solve the problem, at least for a while.