I found that even with a 240v charger connected it would still show low battery for the first 30mims or so of towing.
Since connecting it to the house battery with the charger it's always shown fully charged.
On a similar note, I decided to test my breakaway unit before setting off on our last trip.
Pulled the pin and no alarm.
Put it back in and out again, still no alarm.
Left it out and pulled the van to see if the brakes were on, and again nothing, until I have moved about 2m and then the brakes finally came on.
I think the switch got stuck, so probably worth testing them periodically.