Do you have another email from which you can send one to the problem email to see if the inbox is working properly, at least for that test email? You may also get a reply notification from this community in your Hughes email when this reply posts.
I would change my password, just in case. You never know.
Also, and this is just an idea, but if you don't already have one, you may want to consider getting a new email at gmail or something like that, then forward your emails from the Hughes email to there, just so you could have a backup when you receive emails.
Edit: As for where your emails may have gone, I have no clue, other than possibly someone signing into your email and deleting them. It's also possible that there is some type of email system problem right now. The reps are gone at this point, but when they're back online tomorrow they may provide some ideas and/or help. Some fellow subscribers may, as well.