If your computer running Reflector Teacher doesn't display in the Reflector Student menu, your computer isn't able to see the iOS device for one reason or another.
If you're on a home 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.
Microsoft has included instructions for allowing applications through the Windows firewall here: http://windows.microsoft.com/en-US/windows7/Allow-a-program-to-communicate-through-Windows-Firewall
If you're using a Mac, Apple has provided similar instructions here: http://support.apple.com/kb/ht1810
Computers also sometimes use Antivirus applications for security. These applications can have their own firewalls blocking connections. You may need to make allowances for Reflector 4 within these applications to allow the connection.
Corporate networks often block a number of ports from communicating across networks. You may need to have your IT department allow TCP ports 7000, 47000, 7100, 49228, 50259 and UDP 62572, 54780 to be open to communicate. The network must be configured to run in Multicast and also allowed to run Bonjour and mDNS. It's also common for corporate and education networks to implement segmentation with VLANs or other similar methods.
If you are unable to see Reflector 4 due to segmentation, using the Quick Connect code or the Link with Camera options should allow you to connect. If you are unable to see Reflector 4 due to segmentation and you must use one of these options, Reflector Student will share that connection information on the isolated network segment after it has connected. What this means is that once one device has connected to Reflector 4 using Reflector Student, other devices on that network segment can then use the Auto-Discovery feature to connect without the need for a QR or Quick Connect code!
More details on using the Quick Connect code or Link with Camera options can be found here: Connecting Reflector Student to Reflector Teacher
Apple has provided more instructions on this issue here: http://support.apple.com/kb/TS4215