Have you already checked if your printer's firmware is up to date? Because often wifi disconnection issues on Brother printers are linked to bugs that get fixed in newer versions.
What the others didn't mention is that the wifi module on the MFC-L8360CDW sometimes gets into a kind of instability loop when the initial connection is weak. It's not just the sleep mode - once the connection is established poorly, the printer keeps trying to reconnect every time it finishes a job. What works best is doing a "factory reset" of just the network settings (not the whole printer, just from the network menu) and then setting up the wifi from scratch with the printer literally right next to the router.
Also, check the printer's logs to see if there are authentication errors - access the printer's web panel (find the IP from the network menu) and look at the "Event Log" or "System Log" section. If you see messages like "authentication failed" repeating, the issue is that the wifi is asking for access every time, which means the credentials aren't being saved properly. In that case it helps to temporarily disable any MAC filtering on your router and redo the connection.