My hour-meter also turns on and off randomly. I simply decided to install a mechanical unit inside as this information is not something you really need at the helm. It gets voltage directly from the alternator so counts only when the engine is running.
And for jet42's question - to the best of my knowledge the rpm signal comes from the alternator (there is a terminal called TACH). Do not know exactly the internal circuitry of the RPM meter, but it could be a problem with the TACH signal coming to it - I assume the unit "counts" cycles so a lower voltage will cause the unit to miss cycles.
A less likely reason - not sure how much off your display is but could it be that the belt is slipping?