What are these these networks? /24, /23, /22, /16. I would imagine a /24 since you are saying 3 networks. Are you able to ping across from one of the devices sending to the syslog server? Have you tried looking for the data arriving at the syslog server with something like wireshark? Have you setup a rule on the firewall that you can check for matches on syslog traffic even reaching the firewall? I would think you need to start testing basic connectivity then move to data hitting the hops along the way until you see the break. If you are syslog from devices on the same network, unless you have a local firewall setup that will block all traffic not on the local network on the device, you need to clear the edge firewall or routing as the next logical steps.