It wouldn't be a lost signal.
Rain data is sent as a rolling counter value from the sensor.
The receiving device (Access or display) computes the difference from the last received value with the current value. That difference is the rain amount for that time period.
For example, suppose the current counter value is "123" and it hasn't been raining. That counter value will stay constant until the tipping bucket tips with some rain, then it will change to "124". Now suppose it is raining and the signal is lost for some reason. Let's say the signal was reacquired an hour later, and the counter is now "200". The receiving device will then compute the difference of "76". That translates into "0.76 inches" of rain that accumulated during the signal outage.
This means you won't lose the rain accumulation during a signal outage, but your "rain rate" calculations will likely be goofy.
As for the consistent value of 1.28 (or 128 bucket tips), that's a power of 2. That makes it sounds like a particular bit is getting flipped occasionally in the Access.
I'd definitely ask Acurite for a warranty replacement of the Access.