Turn Arduino on with timer every 24h
One approach would be use of a DS3231 (Precision Real Time Clock) module.  Such modules sell on Ebay for under $1.  Search for ds3231 arduino.

Typically, these modules have a six-pin connector, with pins labeled 32K, SQW, SCL, SDA, VCC, and GND.  As noted in DS3231 specs, the INT/SQW pin is used either for square-wave output or for interrupt output.  On page 13 of specs, in the Control Register section, it says:


  Bit 2: Interrupt Control (INTCN). This bit controls the INT/SQW signal. When the INTCN bit is set to logic 0, a square wave is output on the INT/SQW pin. When the INTCN bit is set to logic 1, then a match between the time-keeping registers and either of the alarm registers activates the INT/SQW output (if the alarm is also enabled).


Initially, you would run a sketch to set up the DS3231: turn on a daily alarm, enable an interrupt rather than square wave, set the current time, etc.  Then, load an operational program that reads car-battery voltage each time it runs, and acts appropriately.

The DS3231 INT/SQW pin would be wired to the gate of a P-channel mosfet that switches 12V power to the Arduino.  The P-fet would turn on when the alarm's open-drain output pin INT/SQW turns on.  The operational program does its business and then clears the DS3231 interrupt flag, to shut down power until the next alarm occurs.  (For debugging, set briefer intervals than a day; for example, once a minute, as described in Table 2, Alarm Mask Bits, on page 12 of specs.)

Typically, the DS3231 draws 0.84 μA when running from a 3.3V battery, or 1 μA from 5V.  See Electrical Characteristics, page 3 of specs.