Does it say "please enter your username and password for the following server" and you are sure you're using the correct information?
This is a common issue when several people from the same office are all connecting to the same cPanel mail server around the
same time, or when your email client is setup to make connections every secondto the mail server.
In Outlook or Thunderbird, you will need to update on all PC's :
Tools > Options > General and disable where it says "check for new messages every xx minutes".
Outlook 2013: Home > Send/Receive Groups > Device Send and Receive Groups
If you do not want to disable it, just set it to check less often. For example every 15 minutes. Keep in mind, the more computers you have checking the mail, the quicker you will hit this limit.
You should not configure email checking less than every 10 minutes. You may be blocked temporarily for 60 minutes when creating too many connections to mail server in an hour.