You can also use a voltmeter to see if your getting a response from the rain gauge. Just touch a probe to each side of the reed switch (voltmeter set to low dc voltage) and flip the teeter-totter. You should see a momentary spike in the voltage reading. If not, then the reed switch is bad.
I had almost the same thing happen as you did, but only after about 10 months of error-free operation. I sent the whole unit back to LaCrosse (still under warranty) and it came back with a new thermo-hygro sensor (rain sensor checked out ok). This worked fine for about another 3 months, then same thing, no rain recorded. So LaCrosse sent me another thermo-hygro sensor, which is still working ok today. They told me to pitch the old one if the new one works, or if the new doesn't work to send them both back along with all sensors (which I didn't have to since the new thermo-hygro sensor is working well). Based on other discussions/emails with LaCrosse, I'm under the impression that something has changed in the internal circuitry of the thermo-hygro sensor and the new one has corrected this. But this is only a guess. BTW, I run wireless.