Earlier today, I had the current iOS 11 developer beta installed on my iPhone 7 Plus, and the current developer beta of WatchOS 4 on my Apple Watch.
I heard that new betas were out, so I started by updating my phone. Then, I went to the watch app and checked the software update area. It would just hang on "Checking for Update..." with the spinning wheel, no matter what I did. I tried restarting the phone and watch, disabling wifi - no help. For a while, it would actually give me an error that it could not connect to the Apple Watch - even though I was able to do normal tasks on the apple watch, which was obviously connected and unlocked.
So I tried un-pairing the apple watch, then re-pairing.
Once re-paired, going to software update says that it's running watchOS 4.0, and that it's up to date. But once I install the beta profile again, it goes back to hanging on "Checking for Update..." or hanging for a while then saying "Could Not Connect to Apple Watch - Make sure your apple watch is nearby, powered on, and not in Airplane mode" - and my watch is on my wrist, unlocked, connected & paired.