What would be the reasons for not being able to ping a mail server?
This is quite the question, as there could be so many reasons why a mail server would not respond to a ping. This includes obvious ones like the mail server being down, name resolution being broken, a bad subnet mask being used, the suppression of ICMP echo messages, etc. The best way to troubleshoot the problem is to run a sniffer like Network Monitor and see what is transpiring over the network when you attempt to ping the server.
Unfortunately, given the general nature of your question, I'm not able to provide you with any specific things you can do to resolve this. But, check the basics and take a network trace and you should isolate this problem in no time.