No not normal! You need to check the battery voltage when stationary and when running. If the battery is less than 12v when not in use it is bad or not charged, it should be betting nearer 14v or more when running or it will not charge when in use.
If it is not getting a charge when running either the rectifier or stator need replacing. The rectifier is a DIY job, the stator might not be if you do not have a lot of mechanical experience. If you don't own a volt meter - take it to someone that can diagnose it for you.