Yes, I agree with
aart, it could be a couple of things. However, what ever the motivation for his departure to the other coop...his absence will surely seal his fate.
The alpha rooster will stay with the hens, and the beta will be evicted since he has removed himself. There may even be some aggression towards the beta from the alpha, as the days pass by. You need to check the beta to see if he is ill. Check his poops for diarrhea, or upper respiratory illness could be a reason. Is he sitting a lot, sleepy during the day and puffed up? Could be an upper respiratory illness at this time of year. Roosters are better at hiding their illness than hens, so do check him out.
If it turns out he is healthy, you will need to give him his own flock. When I had two roosters, there were only 5 hens. So, my beta would spend most of his time with me or my husband, or the dog. But, since the alpha passed away and I increased the size of the flock to 9 hens, he is mostly up at the coop with his wives! LOL!
But, he still likes to come down each day to say "hello" and "got anything yummy to eat?" God Bless and hope all goes well.