Mail.app doesn't automatically check for mail every time focus is put on it's window or every time the computer wakes up. There are several ways for you to configure how, and how often Mail.app synchronizes with servers:
- You can click the Send/Receive mail button
- You can use the Command + Shift + N keyboard shortcut
- You can configure your Mail.app to check for mail every minute by clicking the
Mail menu and then selecting Preferences. Under General change the Check for new Messages configuration.
This way you never have to wait more then 1 minute for mail to be synced. Keep in mind, if you are on battery, this will impact battery life negatively.