With 2 mm/s^2 acceleration, Hermes' 124 day trip from Low Earth Orbit to Low Mars Orbit is impossible.
"Low earth orbit?" a Weir defender might object, "It's all hyperbolic fly bys."
Which is wrong, of course. The hyperbolic rendezvous were extraordinary maneuvers made under unusual circumstances (Watney needing rescue). The 124 day earth to Mars trip preceded the Sol 6 windstorm that stranded Watney. There aren't hyperbolic fly bys either at the beginning or end of this leg of the journey.
"The 124 day trip wasn't depicted in the movie". It was described in Weir's book as well as the movie's back story provided by Fox.
Also Neil DeGrasse Tyson's trailer for the movie. 1:15 of Neil Degrasse Tyson's trailer has Hermes departing from low earth orbit. 2:20 gives the trip at 124 days.
In addition here's a graphic from Inside Science (thank you Pearson Art Photo). I underlined the relevant phrase.
A Weir defender writes "The 124 day mission seems to not include LEO, but otherwise is fine."
This is like saying the 5 hour drive from Spokane Washington to Great Falls Montana seems to not include the Rocky Mountains but otherwise is fine.
The cities are 300 miles apart so a 5 hour drive seems plausible until you take into account that they're separated by the Rocky Mountains.
And so it is with the Hermes 124 day trip. When you're only accelerating 2 mm/s^2, getting out of LEO is huge. Here is an illustration from Mark Adler's answer to the Stack Exchange question General guidelines for modeling a low thrust ion spiral?
Mark Adler's description of above spiral:
Here is an example of a spiral from a circular orbit to escape (C3=0):
This is normalized to the starting circular orbit, where the distances
are in units of the initial orbit radius, and the acceleration is
constant at 10−3 of the gravitational acceleration of the body at the
initial orbit radius. The total ΔV to escape is 0.856 of the initial
orbit velocity, as compared to 1.0 for the rule of thumb. The total
time to escape is 136 initial orbit periods. It goes around the body
about 40 times before escaping.
In Hermes' case the 2 mm/s^2 constant acceleration would be about 2*10^-4 of the gravitational acceleration at the initial body radius, so the delta V would be more than .856 * 7.73 km/s. But I'll be kind and go with this under estimate.
.856 * 7.73 km/s is about 6.6 km/s. At 2 mm/s^2, it would take Hermes 3.3 million seconds to achieve this delta V. 3.3 million seconds is ~38 days. That leaves about 90 days to go from a 1 A.U. to a 1.52 heliocentric orbit. Which isn't doable at 2 mm/s^2 acceleration.
Most of that 38 days would be a slow spiral through the Van Allen Belts. Not only is the 124 day trip from LEO to LMO impossible, but it would also cook Watney and friends.