We rely so much on email, it can be frustrating when it is not working.
Hopefully these troubleshooting steps will get you back on track ...
OS X Mail: Troubleshooting sending and receiving email messages
No this does not help. I did this first. It has been very exasperating for several months. Mail always comes in, sometimes it goes out, sometimes it doesn't. Sometimes it goes out from one account, but not from another. It's worse when the internet connection is slow - but not always. Sometimes only emails with attachments won't go out. Right now nothing goes out- not even a one-line response to my mom. I have gone through these steps several times. I have deleted and re-added the accounts. I have totally given up on my work email account- it works fine on my iPhone, always has, but I can never get it to send off the MBA so I just have to go to the website whenever email comes in.
IDK if I need new system software (I am running 10.7.5), a new email program. (currently running 5.3) or what to do. I have had at least two "computer geek" friends look at it, and I went to the MacShop with it once but of course it worked fine that day...