Can a reference electrode be stored in demineralized, deionized, or distilled water?

NO! 

Sensors that are not used need to be stored in a solution that guarantees that the sensor is ready for use. When the sensor is stored in pure water the salt will be washed out of the junction of the reference cell. This causes the sensor to fail. 

Yokogawa uses the same salt concentration in the wet pocket (during shipment and storage) as is used inside the sensor. For combination sensors we add a trace of acid to keep the Glass membranes active. So, the best method is to keep the wet pocket that was shipped with the sensor and store the sensor in the wet pocket when not in use.