If your mail app checks for new messages more than once every 10 minutes, the app’s access to your account could be blocked. Try signing in directly on the Gmail app. For each item type, use the pop-up menu to select the permission. Click the delegates name, and then click OK. Type the name of the person that you want to add as a delegate, and then click Find. Under Delegates who can act on my behalf, click Add.
Important: If you sign in with OAuth, use your regular Google password.
If you have these problems or can’t sign in, first check to make sure you’re using the right password.