"I wouldn't be dwelling on this if I didn't think it was the dominant mechanism"- B.M. Jakosky

I want all readers to consider two important things. 1) Atmospheres are not round, and they aren't very tight. 2) Mars dust does a lot of weird stuff. It has no Earthly equivalent, not even in the driest deserts, and it is always a factor.

The MAVEN mission to Mars is one of the least understood (probably thee least,) yet most important Mars missions to date. This speaker was the PI of MAVEN till about a year ago, when MAVEN ended its science campaign, yet still serves as a relay for ground probes.

• Slide at 5:50, "The upper atmosphere changes with seasons by an order of magnitude. That means the loss rate changes by an order of magnitude." Basically what he's saying is that in the dusty season, the loss rate of atmosphere skyrockets. This is one of two great discoveries MAVEN made. The loss rate on Mars is not consistent even remotely. To this day, people on the outside looking in still seem to assume that it is. "You can't just multiply the current loss rate by four-billion years."
• Slide at 12:40 shows the second great MAVEN discovery; EUV losses were going at a much higher rate before three-billion years ago. They took a different rate when the atmosphere got small enough that Mars gravity could hold some of it. The start of hyper-fast-atmospheric loss is about as old as the oldest Mars surface, Noachian highlands. The end of that rate, and beginning of the current variable rate, seems to start deep inside the Hesperian. This means that whenever Mars lost whatever dynamo it had, the lions share of the atmosphere quickly followed, switching gears during Earths Archean Era. 
• Slide at 16:40, mostly because it's awesome. You get a really cool image of a big Coronal Mass Ejection (CME). CME's are the penultimate-reason you cant import or release a sudden atmosphere on Mars. 
• Final comments at 25:60. 

I don't know why, but MAVEN seems to be referred to a lot by persons whom have obviously misunderstood everything about it. Every MAVEN lecture I've seen is bits of this one, which I'm confident is the most modern. 

"Despite uncertainties, conclusions about significance of loss to space are robust." In other words the MAVEN team tied-a-bow-around-it, and are very confident that Mars started losing atmosphere the day the ground solidified.