I continue to have this drop down issue where the list disappears in less than a second. How do I fix?

What happened when you tried Firefox's Safe Mode?

By default, Safe Mode disables your extensions and hardware accelerated graphics, as well as some other customizations. That often bypasses many sources of problems and allows you to focus in on the cause.

You also can disable plugins here ( I would leave Shockwave Flash enabled):

orange Firefox button or classic Tools menu > Add-ons > Plugins category

Any change in behavior in this mode?

Restarting in safe mode seemed to solve the problem. Is it now fixed?

Everything?

It was OK in safe mode but not when opened regular.

If you restart in regular mode, I suggest first disabling ALL nonessential extensions. You can do that here:

orange Firefox button or classic Tools menu > Add-ons > Extensions category

After disabling everything that isn't crucial for daily browsing, restart Firefox and see whether the problem is resolved. If so, then you can be very selective about re-enabling them until you find the cause.

You also can disable hardware acceleration.

orange Firefox button or classic Tools menu > Options > Advanced

On the "General" mini-tab, uncheck the box for "Use hardware acceleration when available"

That takes full effect the next time you restart Firefox.

I think the issue is finally solved. I thank you very much for hanging in there with me. Firefox is THE BEST!!

Glad to hear you found it. Can you report which was the culprit? If it's not obvious immediately but you discover it in the next couple of days, feel free to post back here for the benefit of other users who encounter the same problems.

Shall do. And thanks again for hanging in there with my ignorance.