Do you have a single or 3 stage converter/charger?
The single stage converter/charger that comes in some RV's will not fully charge the battery and will overcharge the battery if left plugged in continuously. Check the electrolyte level in the battery at regular intervals if you do leave it plugged in continuously
"The life of your batteries will be longer and happier if you charge them correctly. The best chargers on the market are 3-stage chargers. Use of a good quality 3 stage charger will significantly improve your battery's performance and lifespan. These chargers can be purchased separately or are included as part of many of the better quality inverters. When using a 3 stage charger, battery charging takes place in 3 basic stages: Bulk, Absorption, and Float.
Bulk Charge - The first stage of 3-stage battery charging. Current is sent to batteries at the maximum safe rate they will accept until voltage rises to near (80-90%) full charge level. Voltages at this stage typically range from 10.5 volts to 15 volts. There is no "correct" voltage for bulk charging, but there may be limits on the maximum current that the battery and/or wiring can take.
Absorption Charge: The 2nd stage of 3-stage battery charging. Voltage remains constant and current gradually tapers off as internal resistance increases during charging. It is during this stage that the charger puts out maximum voltage. Voltages at this stage are typically around 14.2 to 15.5 volts.
Float Charge: The 3rd stage of 3-stage battery charging. After batteries reach full charge, charging voltage is reduced to a lower level (typically 12.8 to 13.2 volts) to reduce gassing and prolong battery life. This is often referred to as a maintenance or trickle charge, since it's main purpose is to keep an already charged battery from discharging."
2009 Ford F150 4x4 Super Cab, 2009 JayFlight 22FB