What model of Hughesnet modem are you using? This will determine how to go about toggling the Web Acceleration.
I assume when you said you wont upgrade to Gen5 that you are on the HT1100, sad to say, give up on LiveMail. I personally used that for ages for all my MSN and Gmail accounts and it suddenly stoped working. None of the patches from M$ that "fixed" the issue (due to them screwing crap up) would work for me in Win7. I eventually had to get Office2016 with a new version of Outlook.
That aside, as stated earlier, disabling Web Acceleration would be a good step to take to see if that's causing an issue.
After that, trying a different DNS server would be a good step, probably use the Google DNS on your computer instead just to see if the ISP supplied DNS is an issue.
I asked as to what modem the OP was on, forgetting that he mentioned not wanting to upgrade to Gen5, so no HT2000W.
Does the HN9000 have a Web Acceleration toggle?
I imagine the instructions for doing so on both the HT1000 and HT1100 is the same, no matter which one a person has. I'm trying to find a post that gives instructions for them as I can't remember exactly how to get there with those.
Pretty sure the 1100 is the same as the 2000w now... They updated the WebGUI on that awhile back to match the 2000w.
In that case, to toggle Web Acceleration...
Click on the small i in the upper right.
Then click on Web Acceleration on the left.
Click on Control, and then click on the "Web Acceleration Enabled" to disable it, and do the same to enable it again.
I don't know what the heck is going on with the system control center link, but when typing the address, or even typing it with the http:// in front, it adds a 20% on the end when clicking on it. And I don't know why it automatically adds the /#!/usage on the end, but evidently it still works with that on there. Very strange.
I actually use either one. I just tend to give the link to the address I gave as that's what Hughesnet themselves usually give.
I'm a useless troll with nothing to provide except plug the ports in manually on setup. Again, for years no problem unless I entered the wrong info. One question is are you doing POP3 or IMAP?
Ok... I disabled Web Acceleration and the results are the same. My signal strength is at 127 here on a very cloudy day. I have been focusing on trying to get Thunderbird to work vs Outlook and still no account will work except the one from hughes.net. I have again tried both pop3 and imap. I have logged in to all of my email accounts thru Google Chrome browser and verified that imap is enabled. When I enter the same info in Thunderbird I get an error that my user or password are invalid. I get the same result with my yahoo test account.
There does appear to be some issue with the uplink status. As I was entering this post I was getting a red bar at the top of the screen where it normally give the autosave data.