Push is a function that begins at the server. If the server is not capable of pushing, the app on the phone can not improve upon that. Simply put (and this is not meant to be technically precise, but rather understandable). Getting mail is a function that begins on the client. The client connects to server, asks you got any mail for me? Give it to me. This can only be done on a timed basis as the client has no way to know if mail is waiting or not. So, to do push, the server has to have a way to tell the client "I have mail for you, come and get it". This is done through a connection called a UDP connection where the server sends out a message that he's got mail for you. Now the server doesn't really know where you are, so it just kinda broadcasts it out there and hopes you get it. You usually, but not always, do.
So the server has to be capable of sending the "push" message. Some do, some don't. Microsoft Exchange server does and calls it Activesync. You'll have to poke around your server's site or ask someone at that server's site if push is supported.
I hope this helps.