What could happen to my car if I run it without fixing this issue?

I have a 2001 VW Jetta GL and over the course of ownership, I've replace the same sensor about 6 times at a cost of around $400 each time. When the sensor goes, my car has difficulty excelerating and bucks when I step on the gas. When idiling, it sputters and feels as if it might stall out on me but it never does. I am so fed up with the car that I don;t even want to get it fixed if it won't cause any damage to my engine. I think it's an oxygen sensor so can anyone offer some expertise?