So my phone has started syncing again out of the blue. The only thing I can think of is perhaps there was a malformed header within an email which the Samsung email app choked on. Now that it has aged out, it's started syncing again.
I don't know if this was the exact case as I didn't go through all my email headers, but it's the only thing I could think of being that it's started working again.
If you search on this forum and compare popular web hosting providers like Bluehost, Hostgator and Godaddy you will see many users have such problems with their email apps. First it seems your problem comes from your cellphone. But it is surprising that I had the same problem when I had a web and email hosting account with Godaddy and their customer service couldn't solve my problem and finally I moved my email hosting account to Bluehost and the problem automatically was solved, without any action!