I got tired of the same problem and also washed my vinyl liner in the washing machine but found that it gets beat up after a few washings.
I switched to a polyester fabric liner, availble for about $20 at home improvement/building supply stores. I think the polyester is good because of it's characteristic for drying quickly. It still develops mildew spots but at a much slower rate. Pretreat those spots with stain remover and wash it in the washing machine about every 3 months. My current liner is 4 yrs old.
I think a really thrifty person could get a large polyester tablecloth on clearance and convert it to a liner, however, the weight of my current liner is thinner than most tablecloths. ... View related article.