All of our shared servers have a 30 check per hour per IP address limit. If you hit this limit in any hour you'll be locked out for the rest of the hour.
Solution: You will need to disable the automatic checking for new emails. If you do not want to disable it, just set it to check less often. Keep in mind the more computers you have automatically checking and/or manually checking the mail, the quicker you will hit this limit.
I need multiple users to often check email on the same domain!
If you have a company or business which checks email often, then you will need the resources of a VPS or Dedicated Server plan.