Rank change in QR?

I am generating some relatively large sparse matrices (e.g. 13123 x 11697) and using QR to solve a linear equation. However, sometimes the rank R coming out of QR is different (always less) than the matrix going in. For example, my current matrix (J) is full rank (11697) before QR, but the R coming out is only 11693. Obviously, I can't use the resulting matrix to solve a linear equation.

I don't know if this is a bug in MATLAB (seems likely), or if there is something screwy with the numbers that I am generating. Can anyone think of a reason why this might not just be a bug? Or, how do I report bugs to Mathworks?