Have your changed the battery in the remote?

Yes, I replaced the batteries in both remotes. I also wanted to add that the door operates smoothly and does not bind. Thanks.

If the same thing is happening with two different remotes, that pretty much leaves the receiver that is part of the logic board. It is likely a failed or marginal component is causing the problem. Repair would not be cost effective for a ten year old system.

One outside possibility is interference from something that is triggered when the door is opened. If you have something that gets turned on or responds in any way when the door is opened or movement is sensed in the garage, then investigate that device by disabling it while trying the door again.

Possible candidates are fluorescent lights, some kinds of wired motion detectors, any wireless motion detector, and any alarm system that transmits radio signals on any frequency.

Other than that, it's probably time for a new unit.

Thanks for your help creek side. No new electronics (lights, alarms, etc.) have been added to the garage. I even turned off all power except for the door opener, but no luck.
I finally gave up and bought a new one!