PA-28 Flight Instructor reported while demonstrating a maneuver wind moving the aircraft off the runway centerline resulting in the aircraft landing off the runway.

Narrative

Upon reaching the downwind for runway XXL at ZZZ; I was demonstrating a power-off 180 as per the mission required line items. I was lined up with the runway and had a stable approach coming down the runway. The winds at the time were reporting 030 deg at 6 gusting 11 while the winds reported on the avionics were up to 20knots. With this in mind; I was applying appropriate aileron and rudder correction. Upon rounding out; I was still above centerline and everything appeared to be stable. I proceed3d to flare while simultaneously applying appropriate wind corrections to remain over and aligned with the runway centerline. While I was preparing to continue applying appropriate flaring techniques; a gust of wind displaced the aircraft right of centerline. Upon realizing this; I attempted to do a go around and the aircraft appeared to continue to sink. With not enough performance and airspeed; I was unable to successfully climb and proceeded to lose control of the aircraft. The aircraft began to veer to the left and I responded by trying to go back to centerline. The aircraft felt like the tail struck and I eventually landed left of the runway; in between with the parallel taxiway (1).After the above event; myself along with my students; contacted ATC and were instructed to remain within the aircraft while help were on their way to assist us back to the parking area.In hindsight; I would have wanted to be more vigilant of the winds and possibly initiating a go around sooner if it was possible. That being said; I cannot determine whether this would have been appropriate due to the landing appearing to be stable right up to the point of when the wind blew the aircraft right of centerline at which point the aircraft did not have enough energy to sustain a go around. With that being said; I think a thorough reevaluation of decision making during the pre-flight phase could have helped in possibly avoiding the situation.