Did you ever asked yourself if your website is really online all the time? How can this be checked? After all you can lose business when you are offline.
Those problems is mostly related to web servers only, as mail servers try to reconnect multible times other mail servers which might be offline for some minutes.
Of course you can pay for services like mon.itor.us or montastic.com. Of course they also offer free services, but they are always limited to a certain amount of Urls to connect or they only let you check for connection every 60 minutes where every 5 minutes would be better.
I use Google Analytics for it. Just create an alert with the average unique visitor as threshold and let Google inform you when you go below that value. Than it is the time for further investigation.