Your Manage My Home profile does not indicate what brand or model of garage door opener you have but on most openers the reason a door opens or closes on its own has nothing to do with the opener itself.
You may want to check that you are leaving your remotes where there is no chance of something bumping up against them and sending an unintentional signal, but the opener may be getting triggered from somewhere else as well.
The remotes work at a specific frequency, similar to a radio station, and just like your favorite radio station that frequency can receive interference. Sometimes the opener accepts an interfering signal in error just as your radio will sometimes pick up a different station on the same frequency.
Some sources of interference I have dealt with are old remotes in a drawer with something bumping a button, televisions, satellite systems, a change in local phone or power lines, airports, military bases, sprinkler timers, radios, and a host of others.
When the problem is intermittent, as in this case, it can be hard to find the source. Try to look for any pattern that might help. For example, does it happen on certain days only, or, at certain times of the day or night? Did the problem start when you had a new appliance installed, or your neighbor changed his garage door opener? Many service professionals have meters that can help track the signals as well.
If you are certain that resetting the unit solves the problem for a certain time then it is possible you have a problem with the opener itself. Most modern openers have no manual code changes you can make that might help. They continuously "roll" or change the codes to make the system as secure as possible. If you did a full reset it would involve clearing the memory and if all the remotes reprogrammed then they are okay and the problem is elsewhere.
Check for a damaged wire between your wall switch and the overhead unit. If those wires made intermittent contact it would open or close the door. Also, check that the outlet the opener plugs into is solid and grounded properly as a sudden power surge or power loss might be contributing.
If none of these measures help, you may need a new Logic Board for the opener. Be sure to carefully check all other options first as Logic Boards are expensive and, if you do have some form of intermittent interference, replacing this expensive component may not stop the door from opening or closing on its own.