Diagnosis
This is a power-saving or stability feature in the Bluetooth stack that's overly aggressive, dropping the connection to preserve resources or due to minor interference.
How to Fix It
Forget and re-pair the headphones. Go to Settings > Controllers & Bluetooth Devices > Other Bluetooth Devices. Select your headphones and choose "Remove Device." Then put your headphones in pairing mode and select "Add Bluetooth Devices" from the same menu to re-pair them fresh.
If That Didn't Work
Disable the "Bluetooth Device Power Saving" feature. Go to Settings > Display & Sounds > Power Controls and turn OFF "Bluetooth Device Power Saving." This prevents the Cube from trying to put the audio connection to sleep.
Heads Up
Some headphones, especially older models, have their own auto-shutoff timers. Check your headphone's manual to see if you can disable its own power-saving mode, as that's the culprit.