Hi PassionforFashioin,

The 'falling back feeling' you are experiencing in half twist (ardha matsyendrasana) is likely due to an inability to sit tall out of the sit bones.  The pelvis is being drawn back by either body mass or muscle tension.

Here are some tips to helping you sit taller, thus bringing extra space into the veterbrae as you rotate:
*try sitting with the bottom leg straight forward rather than having this bottom knee bend - you will find that you will have greater ease in setting both sit bones on the ground and less tension will be present in the hip (top thigh) as you twist - this decrease in hip tension will enable a more comfortable hip flexion that generates spinal balance

*consider where you place your foot as the foot crosses over the opposite limb - if you place your foot to close up the knee or thigh, this may create a pulling affect on the hip flexor and lumbar spine.  This unwanted pull can generate a reciprocating rolling motion of the pelvis backwards and a falling motion into the vertebrae - try placing your foot further down the by the knee - also consider placing your foot inside the opposite knee versus crossing over

*if you practicing with a straight bottom leg, engage this limb by mildly reaching out through the heel, keeping the foot angled vertical so the thigh has a slight inwards rotate, and maintaining a light flexion of the foot.  This muscular engagement will echo into the back where supportive musculature will lift the torso and release weight off of the hand behind you

*if body mass is creating substantial interference including difficulty in bending the top knee, consider doing a simple easy pose twist variation instead (basic crossed legs) - you will not receive the secondary benefit of the hip stretch, but you will still engage the spine in a fundamental rotation along with stretching of scalene muscles (neck) and toning of back and oblique muscles

*final tip is to try the bent knee or straight leg version while sitting on a firm cushion - the elevation of the hips will reduce the need to engage the hip flexors and back muscles to erect the spine and bring the vertebrae in balance over the pelvis - keep in mind that you back hand will need to be even closer to the pelvis to prevent the temptation to rest back into the palm

Most important in all seated twist yoga poses is to keep both sit bones grounded in order to sustain evenness in the vertebrae.  Spinal quality is the primary focus.  Always visualize the chest bone floating up directly above the pubic bone as if you were in mountain pose (tadasana).  The more one leans into the back hand and into the back edge of the sitbones, the less space is present for one to twist into and can potentially lead to chronic damage versus healing.

Please feel welcome to read more about how to proper align the spine prior to twisting:
http://www.myyogaonline.com/blog/2007/08/14/hatha-yoga-class-aligning-twisting-yoga-poses/

Namaste,
Kreg Weiss
My Yoga Online