Sending and receiving email on your smartphone is an enormous convenience, so if the email feature fails, it can be an equally significant inconvenience. If your Android's email app just stops updating, you probably have a problem with your Internet access or your phone's settings. If the app keeps crashing, you may have an overly restrictive task manager, or you may have encountered an error that requires clearing the app's cache and resetting your device.
Without access to the Internet, your Android device's email will never update, so you should make sure you're online by looking in the status bar to see if you have a "3G" or "4G" icon to indicate Internet access over a cellular netowrk. If you're trying to get Internet access over Wi-Fi, look for a Wi-Fi icon instead. This icon is a small dot with several lines above it to show signal strength. If you're not online, you may need to move around to find a location with better reception.
If your device's "auto-sync" setting is disabled, it won't ever synchronize its apps, including its email apps. You may have turned this option off accidentally or someone else may have changed it. You find this option in "Settings," then "Accounts & sync." If "Auto-sync" does not have a check mark beside it, tap it to turn it on.
Many developers have created task managers to help you keep control the apps running on your phone. Some of these provide you with many settings, such as automated app control, allowing it to stop or "kill" certain apps. If you have a task manager that's too restrictive, it might be stopping the Gmail app when it opens or performs a certain task. Reduce the task manager's app control or disable the manager entirely; then open Gmail and see if it functions correctly.
Clear Cache and Reset
Sometimes apps will experience obscure errors that persist because of the data stored in its "cache," which is temporary information that makes the app run faster and more efficiently. Clearing the cache won't delete any of your data, like emails or account settings. Open the "Settings" app and tap "Applications," then "Manage applications." Tap the "All" tab and scroll down to your email app. Tap on it and then tap "Clear cache." Next turn off the device by pressing and holding the power button and tapping "Power off." Turn it back on by pressing the power button again and see if the email app is working correctly.