As far as it showing no Rain data, since you are getting info over NOAA network, it does not parse rain since midnight (only 24 and 1 hour figures).
Quoting from question 7 of FAQ @ http://www.wxqa.com/faq.html
The letter “r” followed by 3 numbers represents the amount of rain in hundredths of inches that fell the past hour. The letter “p” followed by 3 numbers represents the amount of rain in hundredths of inches that fell in the past 24 hours. Only these two precipitation values are accepted by MADIS. The letter “P” followed by 3 numbers represents the amount of rain in hundredths of inches that fell since local midnight.
The raw data (link) being reported to your station omits r and p figures, only reporting the P figure which is not reported to MADIS / NOAA.
“…” designates a missing parameter, as per Q.7 from earlier FAQ.
Basically the software you use to update your CWOP station sucks, sorry, if you send me your Davis device ID / mac address, or a link from their weatherlink map (here), I can start updating your station with the proper rain figures included. You will need to disable the updates from Davis software so that it will not cause interference.
P.S. Seems you are having barometer issues (link) as well , though it could be potentially explained by Davis software: