I only use the lines on the cutting mat when cutting strips. Even then, I only use the horizontal ones to make sure that my selvages are aligned and I can true up the non-selvage edges. It is surprising to me how much it can be off.
Strange that you seem to be going to through so many mats. You must be a prolific quilter! I have a mat that is so old it doesn't have a grid on it. It's just green. But I suppose that makes sense if you are using the lines on the mat, you are cutting in the same place all the time and making the groove deeper and deeper.
Good luck!