I have had a similar problem. I don't know if it is coincidence, but I have discovered that if the monitor is fitted a little while before I fire up the Garmin, then the display reads OK. Say fitting it when getting dressed then having breakfast, before going on my bike.
On the other hand, if I fit it just before getting on my bike, then it doesn't always pick up, until I have been riding for a while.
The conclusion I came to, possibly wrongly, is that even if you wet the contacts before fitting, that isn't necessarily enough. There has perhaps got to be a degree of moisture on the surface of the skin, which wouldn't necessarily happen, just by wetting the contacts. There is however likely to be moisture on the skin once the unit has been on the skin for a while, if only because of the plastic back to the monitor.
I had planned on trying a smear of vaseline on the contacts before fitting and then seeing if the receiver and transmitter communicated straight away, but haven't got round to it yet.