Hey hannaahart,
It appears that your AirPods keep disconnecting from your iPhone whenever your Apple Watch receives a notification. We'd be looking for a solution to this too, and we're glad to provide assistance.
Switch AirPods between iPhone and other devices - Apple Support -- It sounds like the focus of your AirPods moves to your Apple Watch because of the notification. Let's see if stopping your AirPods from automatically switching helps. You'll find the steps just above "Choose between AirPods and other playback devices for your iPhone audio".
If that doesn't resolve the issue, please refer to the steps below and test after each pair:
Restart your Apple Watch and paired iPhone starting with the iPhone first
Make sure both your Apple Watch and iPhone are up to date
Unpair your Apple Watch from your iPhone, then set it up again
Feel free to get back to us with any questions or problems you may have.
All the best.