Logic suggests if your battery is fully charged then you don't need to leave the charging system turned on, but the your caravan charging systems should be voltage regulated to prevent damage to the battery if left connected long term.
Technically by 2011, your caravan should have a Switched Mode Power Supply (SMPS) fitted rather than a simple charger circuit.
To confirm if the the battery is charging, do you have a voltmeter you can use to check the battery's terminal voltage? It should be about 13.8V when charging. And if you have a battery in good condition, fully charged, the terminal voltage, with the SMPS turned off, should settle to around 12.8V.
Unfortunately some makes of control do have a reputation for failing, but if that happens, there is a company that literally can repair to better than original.