I had the same problem when it was dry and cold with the basic Garmin HRS and Monitor. I bought a Garmin Premium Heart Rate Strap and Monitor and use a little conductivity gel and that has solved the problem.
Here is a link to the Polar strap that many people say is better than the Garmin strap http://www.amazon.com/gp/product/B000OL06A4?ie=UTF8&tag=dcr07-20&linkCode=as2&camp=1789&creative=390957&creativeASIN=B000OL06A4
The basic Garmin monitor will not work with the Polar strap but the Premium Garmin Monitor will.
Here ia a link to the conductivity gel
http://www.amazon.com/Parker-Spectra-Electrode-Gram-Tube/dp/B0002CA8RQ/ref=pd_sim_sg_2
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