@smitchell4130 

Hi, there is no known incompatibility issue between our range extender and BT router, please check and confirm if the extender is plugged in proper location, if it is too far from your router or receives weak signal from the router, please move it closer to your router.
https://www.tp-link.com/support/faq/2692/

If the problem still exists, please check the LED status on the extender when it happens again, and also confirm if it will recover automatically after a few seconds or minutes, or you have to restart the extender to get internet again.

By the way, may I know if your extender is configured to have the same WiFi name as your router? If so, it is recommended to change its WiFi name to a new different one for troubleshooting purpose so that you could tell which network you are actually connected, then check if the same client device could still connect and get internet access from your router when the extender loses internet access.