I also just encountered this yesterday, suddenly for no reason, I could not connect to Xbox Live (360) while on Series X back compat.
It helps that I'm a MS certified network tech, to figure this one out. Maybe this will help you:
I narrowed it down to NOT being an account issue, because my older Xbox One logged into 360 Live just fine.
I tried the Series X settings under "Storage/Clear local 360 save games & profiles" something like that. Which should re-sync a corrupted profile.
That did not work. It also took a long time, maybe 8 minutes. I then connected via WiFi instead of the Ethernet cable. That also did not work. Made sure router settings are all good.
HOWEVER, I think this below might work for you, in this exact order...
Connect to a "new" network, via phone hotspot or whatever other than your preferred existing connection, and then go to Settings/Storage on the Series X and Clear the Local 360 storage WHILE ON THE NEW TEMPORARY WIFI OR LAN connection.
When I did this, the data sync went way faster (like 1-2 minutes), and I was up and running on my temporary Wifi connection.
Then, when I reconnected the LAN cable after a "good" 360 profile sync (note, I did not "download profile"), it was all working again.
It is now working on the previous IP address (so it wasn't MS marking that NAT IP as "bad" or something).
Make sure your NAT says "Open" under Xbox network settings and nothing weird is going on there.
I was concerned it was a server outage, but it seems like the local 360 profile gets corrupted for some reason (maybe leaving games running logged in to Quick Resume has something to do with this?)
I was about to give up and assume server outage until I tried the 360 profile sync just 1 more time. The 360 profile sync occurs after you've cleared the 360 local storage and then launch a back compat game, you'll see it sync the cloud saves, etc. Do this while on a new connection other than your previous non-working connection, then connect back to that one.
I hope that made sense. Good luck!
I've been having the same issues and no one has been any help. Tried tons of fixes including:
- Cleared Mac Address
- used alternate DNS's (8.8.8.8)
- opened up every port they recommended for Xbox Live in my router settings
- WWM, QOL tagging off/on
- tried wired Ethernet, Wireless 2.4ghz, and Wireless 5ghz
- static IP Address
- set my Xbox to DMZ mode with my router
- Factory Reset Xbox
and still can't play any 360 games on my Series X. Really sucks. Weirdesr thing is that it works fine when using Cloud Gaming so it has nothing to do with my account