Yes. Moving CG farther and farther back will eventually cause the plane to be directionally stable falling backwards. Abusing rearward CG limits is contributory to this condition.
Secondly, poor design of horizontal stabilizer, particularly, lacking sufficient "weathervaning" area, will cause an aircraft to be more susceptible to the unrecoverable "deep stall". With models, this is tested by holding the plane horizontal to the ground and releasing it with no forward motion. The relative wind, being 90 degrees to the wing and tail, means they are both stalled, but the pitch torque from the DRAG on the horizontal stabilizer, the rear fuselage and the trailing edge of the wing should flip the nose down and unstall the plane.
Higher aspect wings and/or a shorter fuselage requires greater tail area for the same pitch torque, AND, a larger weight to surface area ratio (bigger plane) also requires a greater tail/wing area ratio.
Placement of the all important horizontal stabilizer can also affect its performance. If it is in the "shadow" of the wing, as with T tails, a very high angle of attack can limit its ability to create pitch down torque. Downwash from the wing can also affect a "low" Hstab.
Lengthening the fuselage is a remedy for not only wing airflow effects, but also increases the pitch torquing lever arm of the aircraft, enabling the same size Hstab to be more effective.
Thrust angling is also a key factor to assisting in pitch down torque. Many aircraft have their thrust line angled down a few degrees, which helps control pitch up tendency as the plane accelerates.
Choice of sound and proven design is important, as well as keeping CG within limits.