Suggestions:
Open Device Manager
Expand Bluetooth
Right-click your Bluetooth adapter
Go to Power Management
Uncheck:
Allow the computer to turn off this device to save power
Update Surface firmware + Bluetooth driver
Update Surface firmware + Bluetooth driver
Reinsert and re-pair
Regarding RMA:
You should consider replacement only if:
Same issue happens on:
Another Windows PC (Win 10 ideally)
OR keyboard never reconnects anywhere
Otherwise: Don’t RMA yet — high chance new unit behaves the same