I'm having a problem with Exchange active sync account using HTC mail app. When the screen goes dark, the mail app doesnt get any new email. I tested this on 3G and it works. I set the wifi options to keep wifi on during sleep always.
Are you using an open WiFi network (one that doesn't have WPA type security enabled)? I have problems with my corporate EAS email on open networks, and assume it's a security configuration enforce by policy.