Ok, we all know there have been message issues of late. Here are some bits of help that I'm finding seem to work.
First, if you have a Microsoft based email you most likely will not receive site generated emails. Hotmail and Outlook I know for sure. Outside of switching to a different email system such as Gmail, I don't have any further advise for emails.
Edit- Email includes Comcast
Second, for IMs here's what I've started doing and it seems to work. I know I have caught one message that did not send. Before sending make sure you click the Save Copy in Sent Folder. Once you hit send check to see if the message is in your Sent Folder. If it is you should be good to go. Before I hit send I copy the body of the message in case it didn't send. I'm long winded sometimes and retyping sucks.