Basically what the title says. Every time I put my pc into sleep or power off the Xbox Wireless Adapter no longer works until I unplug it from the system and plug it back in. Not really ideal for a TV ‘console’ system. 
Same here. I think it’s an issue specifically with Xbox controllers and the kernel driver. Evidently there are some non xbox style controllers that don’t have that problem in Bazzite. I’ve been thinking of picking one up.
Have you tried using usbreset? You could script it to run upon boot and resume.
Find the vendor major:minor ID of the USB device with lsusb.
$ lsusb
Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub
Bus 002 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub
Bus 003 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub
Bus 003 Device 002: ID 06cb:00fc Synaptics, Inc. Prometheus Fingerprint Reader
Bus 003 Device 003: ID 8087:0033 Intel Corp. AX211 Bluetooth
Bus 004 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub
So as an example, here my fingerprint reader is 06cb:00fc.
Googling around, it seems your adapter might be 045e:02e6? I don’t have one myself.
Try feeding that (or whatever ID is correct) into usbreset.
sudo usbreset 045e:02e6
Does that work? If so it’s just a matter of automating it.
I have about 4 of these XBOX USB Wireless adaptors, and I have never been able to get them working at all under Bazzite, not on any machine I have tested, I just assumed everyone was using Bluetooth, which works great, I might have to try them again now, is there anything special to be done to even get them working?
I was having this issue with a nacon xbox style controller. It seems like plugging the dongle into the charger dock that’s connected to the PC is the only way it will consistently work. No idea why having it plugged directly into PC causes this problem though.
If your controller has a charging dock with a slot under it for the dongle, try using it there. My nacon unlimited x dongle consistently works when it’s plugged in from there.
Not sure about the others here, but mine are all genuine Microsoft USB dongles, and genuine XBOX Series S controllers, no docks, or Nacon gear in my setup, I have other controllers Like the Vader’s with their own USB Dongles, they work flawlessly, but I don’t like the controller’s, I prefer the genuine ones myself, was just surprised the actually Microsoft receivers were working, I will be messing about this weekend I think.
I have this issue as well. On windows, i think the driver for the usb dongle almost power cycles it when you resume from sleep. I have been using BT and have had no issue and ultimately gave up bothering with the dongle. See here: How I fixed my Xbox Wireless Adapter in Bazzite (Linux) ~ DeckFilter Blog
Yes, this was my way of fixing it, I just missed the headphone audio stream you get when using the dongle, but I went and got some Sony XM5’s instead, Bluetooth has gotten really good on Linux.
To be honest, I had issues often with the dongle’s in Windows, it would randomly require me to unplug and reconnect it, mainly on initial boot up, so in this case, Linux is just following the same path but just doing it better 
and more consistently.
I am using the ancient Xbox 360 wireless adapter and on Bazzite/SteamOS I also have to briefly unplug it when the computer wakes up for it to work again. Not sure if it’s really the same issue, but if this power-cycling can be automated, that would be great
Edit: I guess I should revert my HTPC from SteamOS to Bazzite so that I have a chance to tackle these things…