DIAGNOSIS: The Bluetooth module in the grill has a limited range and can be finicky. It's not your phone, it's usually the grill's module going into a sleep mode or having a weak connection.
FIX: Force a reset of the grill's module. Go to your phone's Bluetooth settings and "forget" the grill device (it'll be named something like "Weber Grill"). Then, on the grill itself, press and hold the Bluetooth pairing button (near the control knobs) for about 10 seconds until the light blinks rapidly. Open the iGrill app and try pairing fresh from there.
IF THAT DIDN'T WORK: Make sure your phone is within 3-4 feet of the grill's control panel with no major metal objects in between. The signal is surprisingly short-range.
HEADS UP: The module can be sensitive to extreme heat. If you're trying to connect while the grill is already very hot, it might not work. Try pairing when the grill is cool.