when i shut the airpod case it disconnects from my phone

Let me see if I understand you correctly...

1. You take your fully charged AirPods out of their case
2. You "connect" them to your iPhone and put them in your ears
3. You are sure they are working correctly by hearing some sort of content through them
4. You close the AirPod CASE = empty of AirPods
5. The AirPods lose their connection to your iPhone at that moment

Does that describe your issue?

OR

Is chris_g1 correct when he assumes that your AirPods are IN THE CASE when you shut it?

If I may wheigh in on this, I just got my AirPods and after using them for pretty much the entire day I figured out a couple of things. First of all AirPods (not the case, just the buds) are wireless, not Bluetooth, the Bluetooth audio is actually the case itself which then bounces audio back to the buds themselves so if you happen to be listening to music and you forget the case at home you’ll soon realize they disconnected. The other thing is the case cannot be charging while you’re listening to music on the AirPods. As soon as you charge the case it immediately disconnects the buds.

Sorry if it’s a bit of a late reply, but I figured this is my best guess at it.

Charge your AirPods and case
To charge your AirPods, put them in the case and close the lid. AirPods shut down and charge whenever they're in the case.
You can charge both your AirPods and the case by plugging the case in to an Apple Lightning to USB cable. Learn more about charging.