Manually managing synced items has nothing to do with it, as that's how mine is set, with wi-fi sync checked in iTunes. Once I checked the box (with the phone connected), I hit the APPLY button. Ever since, if my iPhone is on, it shows up when iTunes is opened, and I can drag songs and apps etc. to transfer with ease. Same with my son's iPad and wife's iPhone, whether they're plugged in to the AC adaptor or not... might check your wifi coverage/strength?
Usually transfers quite a bit faster than when connected by the cable, and I save the time of opening the otterbox flap, connecting the cable and waiting for iTunes to recognize the device. Now, once I'm in range, it will find the phone, and it's ready to transfer before I can get from the front door to the computer desk.