Great voltage with engine off. Low end of voltage at 2500 rpm, should not be > than 14.5V. More importantly, have you checked the CCAs? Does your Edge sit for any significantly long periods of time? Phones nowadays can be pulling 2A or more from the battery. And of course the radio will drain a good amount of power as well. The "battery minder" feature may be nothing more than a timer, so I would not depend on that to save the battery. Also, any time a battery drains to the point you have to jumpstart, you need to let the PCM relearn the battery in 2011+ Edge vehicles. Easiest way? Let the vehicle sit undisturbed after a full charge for 8 hours.
General Specifications Item Specification Generator — 3.5L Generator pulley ratio 2.66:1 Rating 70 amps @ 600 rpm (min) to 155 amps @ 2,500 rpm (max) Voltage regulator type Electronic internal with generator Generator — 3.7L Generator pulley ratio 2.66:1 Rating 89 amps @ 600 rpm (min) to 178 amps @ 2,500 rpm (max) Voltage regulator type Electronic internal with generator
If the battery is deeply discharged, it should be charged with an intelligent pulse charger at no more than a 10A rate. Might take a few hours to complete. Will ramp up to 90% pretty quickly then really start slowing from there.
Check the current draw on the battery 40 minutes after you turn the engine and all accessories off. Should be 0.05A or less on a totally stock vehicle.
If you don't have a group 65 battery installed, I would suggest getting one. Gel Cell or AGM preferably. They can withstand deep discharge much better than regular SLA batteries.