EDIT DEC 01 2020: sof_gun's solution worked immediately for me! Saved me a trip out to bring the device in :)
I have this issue too! Apple Support told me to delete all Login Items in Settings and all unfamiliar items in Library/LaunchAgents, Library/LaunchDaemons, and Library/StartupItems. It didn't help though :(
For my situation, I'm suddenly having difficulty connecting my Beats Studio 3 (wireless) and my AirPods Pro to my MacBook Pro (Retina, 15-inch, Mid 2015), and my iMac (Retina 5K, 27-inch, 2019), both running on version 11.0.1.
They connect for a second and immediately disconnect. Both the headphones and earbuds are at a full charge. Prior to contacting Support, I tried forgetting the devices, resetting, checking the firmware, and resetting the Bluetooth module.
I am not having the same issues on my iPhone 11. Both devices were working a couple weeks ago — the only change has been the Big Sur update.
Funny thing — my headphones and earbuds do connect properly to my sister's laptop (same specs). Strange!