Today I learned… In Windows, if a process listens on a port, spawns a child, then dies, then no other process can listen on that port until all of the children have been terminated. So, if you were running, say, PowerShellServer, and a process inside of an SSH session hangs, then you can’t restart it until you hunt down the process.
Thank you Server Fault for the answer, TCPView for telling me that a zombie was listening on the port, and Process Explorer for identifying the orphaned processes.