I have multiple emails accounts but none of them will sync, how do I fix this?

I have multiple email accounts set up to my phone. But one of them, the one that's been connected for the longest time, has stopped refreshing and hasn't shown any of my emails for almost 3 weeks now. But all of the other accounts are fine. I've checked the settings for the individual account and it says that the sync is turned ON. But it mustn't be if the account won't refresh...
Anyone else had this problem or know how to fix it? I have a galaxy note 3.

Welcome to the forums. What email client is it?

And is the account entered as an email account or a Google account? (Many people make that mistake - if it's a gmail address, they enter it as a Google account, and that causes problems.)

Also, can you access the account and get new emails with a computer connected the same way (POP3/IMAP)?