I suggest you wait until the Hughesnet corporate reps on this site see your post and get involved, which unfortunately won't be until Tuesday, since they keep business hours and don't work on holidays. The corporate reps can make certain decisions that it seems the phone reps aren't allowed to make.
Have you power-cycled your modem? Also, when the issue happens, what is the state code? You want a state code of 0.0.0, but when something is going on, you will see other numbers, which indicate what the issue may be. This data will be useful to the reps here.