Simply fit a battery protection board on the battery (or bank of batteries), they are freely available at VERY low cost, and can be sourced for varying numbers of batteries. They prevent over-charging (and resultant fires), prevent over-discharge (and ruining the batteries, plus (if you have batteries in series monitor the individual battery voltages.
Or, assuming the power outage isn't going to be for longer extended periods?, simply stick more batteries in parallel to maintain the power until it returns - if one battery lasts 4 days, then 2 would last 8 days etc.