Generally speaking, and engine that is running okay will die if it loses spark or fuel.
So, the mower starts and runs fine as long as it stays dry, but dies when you take it onto a wet lawn, or what?
I'd suspect the spark plug might be grounding out somehow from the moisture. Inspect the plug, cap and wire carefully for any signs of damage, fraying, exposed insulation, cracked cap, etc.
-Robert@Honda
Caveat: I work for Honda, but the preceding was my opinion alone.
