Apple iThings are notorious for consuming IMAP connections, leaving none for other devices and software. I think you need to ask on an Apple support site to see if you can restrict the number of connections it makes, or make a point of taking your iThings offline while using Thunderbird.

it works fine on my apple ipad and nokia phone. It does not work on my windows desktop.

Turn off your phone. Does it now it work? What Zenos is saying is the phone is breaking it (perhaps in conjunction with other devices like your tablet)

Nope, I turned both off and still the same error message of exceeded maximum # of connections to server. I reduced the cache down to 1. still same error message.

Have you actually logged into the server using web mail. Sometimes that error simply means no connections are allowed because your password is not working for some reason. Like your account is suspended, or Thunderbird is using the app password for another app or you have started using two factor authentication and have not created an app password.