I think you have a receiver problem which is a part of your logic board. Due to the price of the board I would put up with this nuisance.

One additional piece of information: although the hard-wired pushbutton works normally, without the need to hold the button in, immediately after using the hard-wired button, neither of the wireless device works. The waiting period is 4.5 seconds.

Can you ballpark the cost of a new logic board?

The logic board runs around $80.00.

In my last post, I meant to say 4.5 MINUTES, not seconds.

Dons right, anytime a wall button works fine and all wireless devices work intermittently ( no matter what the time frame ) it points to a logic board unless you have an external reciever mounted on the opener or plugged in somewhere else, this could be going out also.