Battery cut-off when battery power falls below N volts

I have an electronic circuit turning on a solenoid at certain intervals. The board has 12V battery backup. During extended power outage the battery runs down to 0 volts and when the current is restored, with the battery stone dead, the charger fails to begin the charge. It is aslo detrimental to the lead acid battery. Has anyone got a simple way to cut the power when the voltage drops below, say 10V? The maximum current draw from the battery is 1amp for 50 second periods if and when required.

I was thinking of using a 555 which is latched manually by pressing a push button instead of the present on/off switch. That can drive a transistor which when it cuts kills all power drained from the battery. Another pushbutton can act as an Off switch by unlatching the 555. I do not have the expertise to make this work and guess there must be better ways.
Help will sure be appreciated.

I would suggest a zener diode, which would stop current flow when the voltage drops below it's cutoff. I think this would be the simplest way to do it.
Hope this helps!
Der Strom

Exhaustive thread on a Low Voltage Cuttoff. I have also posted a variation of this circuit with a PFET as a cutoff. Search for it.