In my experience if your link goes down and your mails get delivered to your web host server, then when the link comes back up, the web host server should automatically try to deliver mails to your exchange server. If this is not the case, then you need to ask your web host server people to set this up for you, which should be relatively simple.
Alternatively, you would need to invest in a POP3 download program to pull messages from the web host. I have used POPCON before - it is simple and relatively trouble free, but I am sure that others exist.
http://www.christensen-software.com/popcon.htm