Has anybody else noticed that their Copen shakes when the fuel tank is empty? Initially I thought that I had a slow puncture because the car was making a rumbling noise and shaking abit, and I'd check it out when I went to fill up with fuel. Looked all around the car and no sign of any problems with the tyres. Filled the tank to the top (32 litres) and off (after paying) ;P. The shaking and noise stopped. Do you think that given the size of the car in relation to the petrol tank, that the weight of the fuel 'dampens' the suspension and stabilises the car?
I have the 660 same as you, but I can't say I've noticed any rumbling or shaking when the tanks empty. I'd suggest getting in the air to have a look at the suspension. Did the car have a fresh MOT when you bought it?