I have the exact same issue on my 06 LR3. Works perfectly sometimes then just stops. Very annoying and random. I probably just need to replace the sensor. It's really easy I believe.
Resurrecting an old thread, but I had to post this as it had been driving me nuts for ages.
Had the same issue with my RRS. Sometimes it worked OK, but as often as not it would either refuse to wipe, or wipe continuously even under very light rain. Sensitivity settings seemed to be "Never ever wipe"->"Never wipe"->"Wipe if there is a cataclysmic flood"->"Always wipe, sometimes frantically"
The dealer actually replaced the sensor under warranty which improved things, but only slightly.
After poking around in an online service manual, I found this nugget under Diagnostics for the wiper system:
If a rain sensor fault prevents the sensor from operating, the BCU will control wiper operation as if a
rain sensor is not installed in the system.
So, I just unhooked the damn thing. Sure enough, it reverts to regular old foolproof intermittent mode, no reprogramming required. Controls will work exactly like you expect, with the "sensitivity" adjustment now controlling delay. It's a 30-second tool-free job; snap the plastic cover off behind the mirror, pull the connector out of the sensor module, and put the cover back on. Service manual was for an L322, but I can personally confirm it works in an L320 RRS, and I'd be shocked if it didn't work in an LR3/4.
The light sensor for the headlights is in the same module, so you do lose that feature as well. The headlights will revert to always-on when in the automatic position - the truck basically just thinks it's always dark out. I was fine with that compromise, YMMV.