If the AirPlay mirror icon isn't displaying, that means your iOS device isn't able to see the computer for one reason or another.
Your iPad, iPhone or iPod must be on the same network as the computer running Reflector 3. If you've already made certain the devices are connected to the same network, the firewall on your computer may be preventing the devices from communicating. It's also possible that the firewall on your router is preventing communication.
Some wireless routers prevent communication between wireless devices and wired devices. If your computer is connected to the network with an ethernet cable, try using wifi instead.
You can find some instructions for allowing applications through the Windows firewall here:
If you're using a Mac, Apple has provided similar instructions here:
Networks must be compatible with Airplay. It is common for corporate networks to require some minor adjustments to allow for AirPlay discovery and connections. The document linked below details all of the networking requirements for AirPlay discovery and connections. Your corporate network's IT team can use this information to ensure that your network fully supports Airplay.