Ken, it does get power from the battery. But if your battery is not up to the task then you need some auxiliary either by having shore power and the convertor running or plugged into the truck and that running.
It is not a question of your battery having enough juice to run the jacks up, rather the electronics in the LevelUp need to see a certain voltage to operate correctly (as far as the brain is concerned).
Even if the system will not operate automatically it will still operate in the manual mode, overriding the system need for "X" amount of voltage.
Personally, I think the LevelUp's required voltage reading may be a bit high. But, it may be that way because of the electronic sensitivities.
That all said, the battery in your trailer did not come from Heartland, it was installed by the selling dealer. Odds are it is a rather inexpensive battery with a low reserve capacity.
Something to keep in mind, the batteries we use are capable of having a proper voltage reading but could in fact have no reserve capacity.
An example would be that you read with a digital multi-meter 12.6 volts across the battery terminals (typical fully charged wet cell battery).
But when you turn on a draw, say all the trailer lights, the voltage drops down to 10 or 11 volts.