This is a partial answer, pertaining to the wifi problem. Upon re-reading the question I understand that the device may not appear when connected via USB either. I'm waiting for more information from the OP before tackling that. Meanwhile, this will be helpful to those suffering from the wifi sync issue, and might resolve the OPs problem:
iTunes not seeing the iOS device(s) is a fairly common and annoying problem with wifi syncing. I'm uncertain as to if it's a true bug or is a system conflict within certain environments.
First, you absolutely do not have to nuke your entire iTunes setup.
Generally you can get iTunes to recognize the missing devices device(s) by opening Activity Monitor (Mac OS) or Task Manager (Windows) and killing the AppleMobileDeviceHelper service. Note: you don't want to uncheck (remove) the service in Windows, you just want to kill or restart it.
If that doesn't work, you can connect the device to the computer and use iTunes to deactivate, then reactivate sync over wifi. You need to apply the changes for both actions—just clicking the checkbox twice in succession won't do it.
Neither of these solutions are permanent, though I can sometimes go months without a reoccurrence.
Apple Knowledgebase: iTunes 10.5 and later: Troubleshooting iTunes Wi-Fi Syncing
OS X Daily: Wi-Fi Sync Not Working? Here’s How to Fix it for All iOS Devices