Assuming the Tx is the ONLY common piece in the game, then yes. Looks like some kind of Tx issue. But if you're also moving the Rx from plane to plane, then the problem could be there too.
I'd suggest setting up a system on the bench. i.e. Rx, servos and battery. No model. Then go through the set up on the Tx as if it were a new model. If the elevator works, then you may only have to go through each model and set it up again.
Also, are there software updates available for the Tx? Did you discover the problem BEFORE doing any updates? Try making the updates and see if that shakes things loose.
Another possibility is the connector(s) inside the TX for the elevator channel. Pop the case open and have a look. Start at the stick and follow the wires. Disconnect and reconnect any connectors you come across the idea being to correct for loose or corroded pins. Examine the pins and look for corrosion. If you find corrosion then the entire Tx becomes suspect and I'd have to think long and hard before using it on anything that flies.