Can't use 2nd remote

Greetings all!
I have a typical setup: Craftsman 1/2HP (model 139.53916D), one hardwired wall switch, one exterior keypad and two remotes. The remotes that came with the unit back in '09 were two Craftsman 315 (model 139.53752 and 139.53753). Those were replaced with a pair of Clicker KLIK1U that have worked for nearly a decade.

One of these remotes started to react sporadically, then stopped working completely. New batteries and the LED indicator blinks when the buttons are pressed. The main unit refuses to learn the new remote. I can wipe out all configurations and start from scratch at will, but the main unit will only learn the one remote that worked before and the remote keypad. I dug out the original remotes: no luck. I bought a Chamberlain Universal 2-button from Home Depot: nothing. I bought a NOS Clicker KLIK1U, just like the pair that used to work: still nothing. The main unit refuses to learn any remote except the one older Clicker and the remote keypad.

Any other ideas?

You've tried various remotes, even NOS Clickers, but your opener only learns the old Clicker and keypad. Here's what to explore:

Opener: Double-check "learn" mode instructions and reset the opener. Inspect the antenna connection and receiver board.

Remotes: Test them on another compatible opener if possible.

You can also try other potential methods like: 
Move opener/remotes away from potential interference sources.
Research highly compatible universal remotes based on your opener.
Consider professional repair/replacement if the receiver fault is suspected.