It's possible your battery was bad, it's also possible your converter/charger is going bad. From what you describe as your usage the battery should have made it for the weekend.What you experienced though sounds like the charger is not doing it's job.
Unless you provide a way to keep the batteries topped up, you should always disconnect the battery from the trailer when not in use. A fully charged battery will drain down in about two weeks from parasitic loads in the trailer. (smoke detector, lp detector, refrigerator board, etc). I usually pull the ground wire to disconnect. Some people install a disconnect switch.
If the trailer is at home try checking the battery voltage while not plugged in. Then plug it in and check the voltage again. Voltage plugged in should be in the 13.5v or higher range.
You can also charge it up for a couple of days and then disconnect the battery so the parasitic loads can't drain it. Then wait a week and check your voltage. It should still be 12.6 or higher. If not it's either not fully charged, or going bad.