No, not only running the car will charge it. This generation of vehicle uses an advanced charging system (aka Ford BMS) where it mostly charges the battery in deceleration events to eek out a little better fuel economy, and perpetually keeps the battery at a lower state of charge to accomplish this, but also can't drain too low because critical high current features like the electric steering depend on it.
This state of charge level can be programmed, and it also changes the charging algorithm based on battery age, battery voltage, type and capacity of the battery, and shuts subsystems down when the battery does not appear to be functioning properly.
The first thing to determine is what is the parasitic drain level once the vehicle has entered its lowest power state, which it will time out to, perhaps in an hour since you mentioned that interval previously, or it could be shorter than that for certain subsystems.
It is sensing a lower than normal battery voltage based on the driving conditions it's been in. The important thing is to determine why. Maybe you have an intermittent rear wiper failure, or seat adjust, or flaky door latch switch, leaky diode in the alternator, or are leaving something plugged into the cigarette outlet that continues to drain the battery... but whatever the cause, either you have a continued excessive battery drain, or your battery is wearing out. Taking it to get a cranking amps test done is another thing to try. It could be charging up to an acceptable voltage so your charger stops (as it should) but has low current capacity and droops in voltage under a load.
There's more info out there about the Ford BMS (battery monitoring system), here's just the first video I came across:
It seems odd to me that you mentioned that you would charge the battery (to the dealer) and without any specific reason why you might have caused it to excessively discharge enough to need external charging, the dealer didn't indicate that you should not have to do this and that it's a sign of a problem... a problem they should have offered to fix.