Water Sensors Outdoor Analog
To begin with, there are several technologies for water sensing, with varied degrees of robustness. See these questions: Are there existing electronic sensors that can sense if underwater or not? and How does this soil moisture sensor work?, as well as some others on this site.

Some of these options, including a variant on the Grove sensor in the question, can be made robust enough to last years - simply by environment-proof epoxy / conformal coating of the entire sensor circuit other than the sensor strips themselves. This is one of the methods used by remote weather monitoring stations. 

The soil moisture sensor is particularly attractive, as those are designed to be deployed for years of operation anyway.



Given that it is rain that needs to be sensed, an alternative approach would be this:


Place a microphone close to a window or touching the attic ceiling (if an accessible attic exists) of the house to be monitored.
Capture the sound, and code a set of filters and thresholds such that a trigger is generated on the patter of raindrops
Use this trigger to actuate pumps or other equipment, or even to send captured images back to you for post-facto verification.