To manually refresh a folder check out this post:
If automatic sync does not work please check the settings…
Settings > [Account] > Fetching mail > Folder poll frequency
Settings > [Account] > Fetching mail > Poll folders
For a guide on how to configure Push see the following post:
If all of that doesn’t help, please let us know more about your account. What protocol are you using? IMAP, POP3? Does manually refreshing the account work? What sync mechanism are you using?