I'd like to share my experience with this thread. It may help others to work around this Apple nightmare.
If I click on the "Devices" button next to the "Done" button in the main iTunes window, select my iPhone 5 and then click on "Sync" in the window containing my iPhone info, iTunes says it's looking for my iPhone, then my iPhone drops from the list of devices. All that is left is my iPad. The only way to get it back in the "Devices" list (which, actually, now says "iPad," since it is the only thing left after iTunes decided to remove my iPhone), is to connect my iPhone via the USB cable (or use Windows services - explained below). Arghh!!
With my iPad being the only device left recognized by iTunes, I can initiate a sync via my iPad, by clicking on "Sync Now" Under General -> iTunes Wi-Fi Sync. It completes successfully. Subsequently syncing from my PC also works. Upon closing iTunes and reopening it, my iPad no longer appears as a device in iTunes. Either connecting to the PC via USB cable or first shutting down iTunes, then going into "services.msc" (type this in the "run" field in older versions of Windows or the search box in Windows 7), restarting the "Apple Mobile Device" service and then restarting iTunes, makes it appear in iTunes again. This also makes my iPhone reappear. Weird!
But, strangely, after getting both my iPhone and my iPad to reappear in iTunes, I can initiate a sync with either one via my PC without either of them disappearing!! Very inconsistent! but, at least, now, I know how to get them to reappear in iTunes.