I took a step ladder, placed it in a shady spot at the side of the house, and hung my matt for almost a month.....the smell finally left. I had washed it with a Dove detergent mixture prior to hanging it. I thought I had lost a bunch of money, but eventually, the smell did leave and my matt has been use for over two years now with no return of the "rubber base" smell.
Oh yes, I also sprinkled baking soda liberally over the matt to help soak up some of the smell. Still, I think the warmth of airing it, did the job best......
Good luck....don't give up :-)