Battery drain, possible issue with alternator?

MY car won't start due to constant battery drained. I took the battery for recharge twice and later swapped it out with a new battery. Yet, the new battery only worked for 3 day and shut off. I don't know what exactly drains the battery. What could be the cause?

Check the alternator output with a multimeter at the battery posts on 20 volts dc setting if the voltage is not at 13.5 to 14.4 with engine running the alternator is toast.

Electrical problem
1990 Nissan Maxima 6 cyl Front Wheel Drive Automatic 25000+ miles

I think the voltage regulator is draining the battery because the battery is too weak to turn over the battery after we go into the store for awhile (1hr - 2hr) but my husband tells me it couldnt be the voltage regulator. What is your opinion on this?

The battery cables have been tight and clean but I will check the alternator. Thanks!