is there any information in the log when you restart?
what kind of station?
which amount of rain is wrong - today, this week, this month, this year??
what is recorded in the database?
usually the answer to problems can be found in the log and the log is always the first place to look.
when weewx starts up it tries to retrieve data from the weather station between the last recorded archive record and the current time - so the time on the station AND ON THE PI must be correct. If you are using the fake hardware clock you are probably asking for trouble. Weewx should not be started until the rpi has got the correct time set. Later versions of weewx are pretty good at this - but the issue is only really resolved by having an RTC installed.
Sorry to waffle on a lot - start with looking at the log.