I was having this problem with a windows UDP socket as well. After hours of trying everything I finally found my problem was that I was calling socket(AF_INET, SOCK_DGRAM, IPPROTO_UDP) on the main thread to create the socket, calling bind(...) and recvfrom() on a worker thread, then after closing the worker thread I called closesocket(...) on the main thread. None of the functions returned an error but tor some reason, doing this leaves the UDP address/port combination in use (so a future call to bind() triggers error 10048 WSAEADDRINUSE and netstat -abot -p UDP also shows the port still in use until the whole application is closed). The solution was to move socket(...) and closesocket(...) calls into the worker thread.
Other than weird issues like the case above, there is normally no way that a UDP server socket can be left open after calling closesocket() on it. Microsoft explains that there is no connection maintained with a UDP socket and no need to call shutdown() or any other function. Usually the reason a TCP socket is left open after calling closesocket() is that it wasn't disconnected gracefully and it's waiting for about 4 minutes in TCP_WAIT state for possible additional data to come in before it actually closes. In the case above, netstat showed the UDP socket never closed until the application was closed even if I waited 30+ minutes.
If you're using a wrapper around winsock like the .NET framework, I've also read some features like setting up async callbacks can leave a UDP socket bound open if you don't clean up the callbacks correctly, but I don't think there are any such features in the win32 winsock API that can cause that.