The quasi-rectangular meshes are local modification of rectangular meshes including T-meshes and L-meshes. The splines over quasi-rectangular meshes are involved in many fields, such as finite element methods, CAGD etc. The dimension of a spline space is a basic problem for the theories and applications of spline. However, the problem of determining the dimension of a spline space is difficult since it heavily depends on the geometric properties of the partition. In many cases, the dimension is unstable. In this paper, we study the instability in the dimensions of spline spaces over quasi-rectangular meshes by using the smoothing cofactor-conformality method. The modified dimension formulas of spline spaces over quasi-rectangular meshes with simple T-cycles are also presented. Moreover, some examples are given to illustrate the instability in the dimension of the spline spaces over some special meshes.