Well, a couple of things you can try:
- Try a forced restart: Simultaneously hold down the Home and On buttons until the device shuts down. Ignore the off slider if it appears. Once shut down is complete, if it doesn't restart on it own, turn the device back on using the On button. In some cases it also helps to double click the Home button and close all apps BEFORE doing the restart.
- Sign out then sign back in to your email accounts
- Change the default account, check the status, and then change it back