30% of 12.6 volts is approximately 3.78 volts. Is this what you are measuring?
In any case, you're correct in assuming your on-board charger should have kept the batteries at a full charge or better...typically a float to absorb charge is 13.2 to 13.6. So, it seems either you have the batteries disconnected from the system, or your charger isn't working properly.
With the TT plugged into shore power, what is the voltage measurement on the batteries? If Charger is working, you will not measure less than 13.2 volts. If the batteries are very low to begin with, the charger will be putting out over 14 volts.
Make sure your battery disconnect switch is in the on position. Measure and let us know what you find.
Ron