This problem haunted me for years until I looked at the issues more closely. Driving most of the day just left the battery quite depleted. Even if I turned the frig on to propane
it would not charge worth beans.
Orlen is right: voltage drop. Think of voltage as pressure: If the battery has 12.6v in it and is being charged by a voltage from the tow vehicle at 12.4v the battery would actually slowly discharge because its "pressure" is more than can be gotten from the alternator.
A decent converter will charge the battery at something like 13.6 volts, enough pressure to force the electricity into the battery at a decent rate. What you need is something similar from you vehicle's charging system.
I eventually decided to put in a "battery minder" (Xantrex Link10). It told me everything I ever wanted to know about what was happening, so I was able to come to some conclusions.
Remedy: 6 gauge charge and ground wires all the way from the battery in the tow vehicle to the batteries in the trailer (through a switchable isolator relay). This is thick and stiff wire and not a pleasure to deal with. Incidentally, I changed the usual 7-pin into a 9-pin Pollak connector between the vehicles. I needed the extra pins for 3rd brakelight, backup light
, etc. and it came with the bonus of 2 connectors which would actually accept the 6-gauge wires. Apparently truckers use this connector all the time. Other than the 9 pins, which are longer and make better connections, the housing and plug look just like the usual 7-pin.
Result: Let's say I leave the campground with a percentage battery charge somewhere in the low 70es. After an hour or two of driving the percentage charge in the batteries has gone up maybe a dozen percentage points. This is with the frig running on 120v through an inverter plus a towel warmer on (43 watts). The difference is huge from the non-functional earlier situation.
Conclusion: If you want to get the batteries charged while driving you have to deliver the extra voltage, and the only way to really do this is with hefty wiring. 6-gauge may be more than you need, but by the time you get to 10-gauge I suspect thing get marginal, especially with a long wire run.