@Lukas_K
Hi, is your extender working on Range Extender mode or Access Point mode? and is there any changes on the LED status when the problem happens?
If you mean Ethernet connection between the extender and your computer, please try to ping your router LAN IP address and also ping the extender IP address on your wired computer to see if ping stops working at that moment.
How to Use the Ping Command
Note: For continuous ping, the command is "ping xxx.xxx.xxx.xxx -t"
In addition, please also connect the same wired computer to your router with the same Ethernet cable to see if there is any similar issue, and check if the Ethernet cable is in good condition, try different Ethernet cable if available.