There is a place for the ORS, and for yielding to bit pressure, etc., however, once it's taught, there's not a whole lot of need to harp on the skill. There are also alternative 'emergency brake' techniques out there worth understanding. Whether the flexion exercises are the cause of your mare's problem or not
, I would take the focus off of the neck flexion, and work more on correct full body lateral flexion. True and correct lateral flexion involves the entire length of the horse, and begins with the hind end, not the reins. I will agree with CA's assertion that lateral flexion is the foundation for vertical (here I mean longitudinal, down the entire topline; NOT vertical flexion of the face/poll alone as CA presents it), but to focus the lateral/longitudinal position of the neck without paying any attention to the rest of the horse is useless at best, and detrimental to the horse at worst. Flexion and suppleness involve the entire horse, not the head and neck alone.
To get TRUE and COMPLETE lateral flexion, practice riding correct circles, serpentines, figure-8's, etc. The curves of these figures, when ridden and set up properly, allow the horse to laterally flex her entire length, not simply isolating the face's position. Use your weight and leg aids to position her entire body around curves and corners - use your reins to support the total curve, not to create it. As she becomes more flexible down her entire length on both sides, she will be better able to stretch longitudinally, from tail to muzzle.
As far as laterally flexing the neck at a standstill goes - what does it accomplish? Not an ORS, since there isn't any motion to stop. All you're doing is turning her face one way or another, something that can be accomplished with much more meaningful and helpful exercises that supple the entire body.
Hope that was somewhat helpful to you. Good luck!