Is the port being filtered/blocked by network security?
Any recent changes to your network security?
Nmap is a great tool to test this:
nmap -sU -p161 <server IP> (you will need either to run this in an elevated admin command prompt or sudo, depending on your system)
Wireshark will certainly give you a better idea of what is going wrong, if you can filter/interpret the packets captured.
Have tried restarting the SNMP service/daemon on the server that is failing SNMP polling?