Your furnace fan draws about 8 amps of 12 volt power every hour or actual run time. In addition to that your fridge, LP/CO monitor draw a small amount of power continuously. Lights, water pump, tv, USB chargers for phones, etc. will all draw power from your battery.
Based on that a simple group 24 battery may have 40 usable amps so that 8 amp draw while the fan is on will eat up the battery capacity if you can't recharge it.
Get a simple battery monitor to make sure you don't go below the safe minimum before harming your battery. 12$ on Amazon, plugs into the cig socket. Read up on battery care information -- https://www.rvtechmag.com/tech/22_batteries.php
Most people agree anything under 12.0 volts will damage the battery in the long run.