The Mail application contains a teriffically useful tool called Connection Doctor. This can help identify the source of your email woes. The following article contains a host of good information regarding potential results from Connection Doctor, and how to go about addressing them.
Open Mail Connection Doctor
In Mail, choose Window > Connection Doctor.
Tip: If you see a spinning gear in Mail or the Mail Connection Doctor, choose Window > Activity to learn what Mail is doing.
All the best,