Bluetooth Headphones are Paired but Cannot Connect without Rediscovering

I have a Windows 10 machine and Sony Bluetooth headphones. I can pair them as usual, and after pairing them I can connect them and play music on them as usual. After restarting or waking from sleep, the headphones stay paired in the Bluetooth devices. There is a button to connect them, but whenever I do that Windows says it can't find them. I have to make the headphones discoverable again and pair them again every time. This is only true of my Windows 10 machine. My phones and tablets have all been able to reconnect to these headphones without needing to pair them again. Others have had this p

Question by Aaron Bramson on Super User, licensed CC BY-SA. We show a short excerpt and link to the original thread as credit.