I've had an issue recently when riding my otherwise good 1x11 Shimano 105 setup. I was tending to get stuck in the lowest gear, the biggest cog. Now admittedly the Wolftooth DM is at the limit of the cassette size it will accommodate, but is has worked OK so far, so I don't see any reason it shouldn't keep working.
I checked everything, cleaned everything and made sure the cable was moving smoothly. I realised that I'd cut a slightly short piece of gear cable to connect to the derailleur itself, so replaced it with a longer one.
The problem didn't go away.
Changing down the gears resulted only in a rumbling clicking sound and sometimes, eventually a shift. I got the bike up on the stand and had a closer look.
I noticed that the derailleur jockey wheel was so close to the large cog that the chain was catching on it and unable to move. I had a vague memory about there being an adjustment for this called the "B-screw" so tried adjusting mine only to find it was screwed all the way in but obviously wasn't doing the job any more. Maybe it wore down or became slightly damaged.
Noticed the B-screw had underneath it a black plastic washer. I took it out and found it was 1-2mm thick. Without it the screw would go in a little further and keep the jockey wheel away from the cog (see above). Proper shifting once more! I'm a little concerned that this washer must serve some purpose, but everything seems to work fine without it.