What type of Garmin HRM strap is it? The older hard plastic one, or the newer premium soft strap?
And checking the obvious, are you actually wearing the heart rate strap while trying to pair it? Otherwise it won't work.
It seems the newer Garmin HRM can be unreliable. This may be caused by corrosion on the contacts. So cleaning them may help, or replace it with a Polar strap as that DC Rainmaker link says. Note you just need the actual strap, not the transmitter as well (the Polar transmitter won't work with the Garmin).