Alternators only output about half the rated amps at idle speed, so a 70 amp rating will not produce 56 amps at idle, which means the battery has to carry part of the load, which is why the system voltage drops below open circuit battery voltage.
Full rated output is usually achieved by about 2000 engine revs. Also, alternator output is less the colder it is (open circuit battery voltage also drops in cold weather), so a high electrical load may mean the battery is discharging. Alternator output is typcially rated at 80 degrees F. If system voltage is less than about 12.5 volts the alternator is not producing enough current to carry the load and the battery is discharging.
Especially if you drive short trips in cold weather with a high electrical load the battery may end up loosing charge. The cure is to reduce the electrical load or drive longer/farther.