If it's the original battery, which seems unlikely, with a car, ten years old, but it just may not be holding the charge anymore. Or the other factor the alternator, being rebuilt, rather than new, may not be doing the job, as it should.
Or something else is draining the charge in your battery. But the Alternator, should be able to keep the charge up, as long as you are driving enough distances each day.
It usually takes about five miles to recharge your battery.
You may need a good mechanic to do a good job, on his scope, to see if all is still in good working order, But something isn't' working right, and I suspect the Alternator, isn't working well, when you are getting that much variation in your voltage.
