I would not want my batteries to get below the 50% charge state point which is around 12.05VDC. The 11.8VDC is right at the 40% charge state. The 10.5VDC is considered a dead battery.
11.8VDC would be my 'absolute' minimum still using the batteries and only for rare occasions. Experience tells us the batteries do not do well when dropped below the 50% charge state point...
I normally switch mine off-circuit when they hit the 12.0VDC level or start my Charge actions then...
In my off-road ops we can do around 10-12 50% to 90% charge states before having to recharge the batteries to a full 100% charge state and not do noticeable harm to the batteries. After that the batteries start falling back on performance and will eventually do harm to the batteries unless I get them fully charged again real quick.
Roy Ken