If you have a typical WFCO converter, not good for the battery to leave permanently connected and on. We found out the hard way and had to replace our Interstate battery after about 2 years old because the WFCO converter killed it (while away on a long road trip). The converter had to be replaced at the same time too 'cuz it failed. Now have a nice Progressive Industries converter.
Get a good battery tender and disconnect the battery from the TT. When you say you turned it off, 120 volts or 12 volts? Your TT will have some parasitic loads like propane detector, radio, etc. that will drain a battery in just days. A simple way to monitor the condition of the battery is with a voltmeter.