Not that I know of - the benefit of webmail is it is done using something firewalls don’t usually block. If I were you I’d check to see if the cookies webmail uses were being saved by your browser - it sets 4 of them. You would have to leave the site, delete any exists cookies from it, and then return and log in, then check to see if the cookies came back. If they do and your still have the problem, try using a different browser and see if you get the same problem. If both browsers have the problem then I would ask Support to look into it.
I thought of something else, too - the webmail will timeout your login session if you don’t use it for a period of time. I couldn’t find anything that says long much less change it though.