My last flight involved some stall training in a PiperSport LSA, and it actually did take considerable conscious input to make the plane move past that "mushy" stage and depart completely (it would nose down quite handily when you did though).
I concur with other answers; there is a difference between a "stall" (exceeding critical angle of attack and thus losing lift and/or full attitude control) and a "departure" (losing most or all attitude control). If pulling back on the stick or yoke won't continue to pitch the nose up, you've stalled, but you haven't departed completely until you can't push the nose back down (or it noses down even with full nose-up elevator applied).
Many small planes with "normal" or "utility" category ratings (or "limited" light-sports) are designed with a large amount of "departure resistance"; their aerodynamic design and mass distribution makes it hard to fully depart the aircraft and enter a nose-down stall (or a spin, spiral dive etc). This also makes intentional maneuvering near the edges of the flight envelope more difficult, as the plane will want to settle back into a stable configuration rather than let the pilot potentially push further into departure.