Hi Forrest
I'm not suggesting there's no a problem, clearly there for you however, my emails come in swiftly.
I have a single customer facing email address my clients use to submit tickets. They are handled by gmail, which forward them on to the relevant gotoassist service email address depending on the clients domain.
Are you using the gotoassist email address, or are you using a 3rd party email service to forward your emails on to the service desk?