The disconnect solenoid should be operational down to 11.5VDC. If you are getting 12.1 at the batteries, you have several possibilities:
• the solenoid contacts are closed and the battery is getting voltage from your converter. The converter is bad if it is only giving you 12.1 at the batteries.
• the solenoid contacts are open and the battery is not receiving charge from the converter. The solenoid is bad and should be replaced.
•*the solenoid contacts have been closed, your battery has been getting charge but is not retaining the charge. The battery is bad and should be replaced.
When you activate the solenoid switch, you should hear a definitive 'click' as the solenoid coil is activated and the contacts either open or close. Up usually closes the contacts and down usually opens the contacts, disconnecting the battery from the 12VDC trailer wiring.
Let us know how you make out with these tests.