No one mentioned the physics behind your problem so I will try.
The single battery would be providing 2x the current than the others, therefore it gets discharged faster and deeper than the other 2. It also gets charged 2x as fast. The result is that it fails sooner than the other two.
You could run this way if you switched the batteries every few weeks so that all the batteries were in the single position for the same length of time. You should also monitor the single battery so it does not get discharged below about 6.05v, equivalent to a 12v battery discharged to 12.1v.
Probably easier to use 2 6v batteries.
