This statement, older women run a higher risk of bearing an autistic child, really means, "More children born to older women (than to younger women) are diagnosed with autism." However, we do not know how many children are born with autism (or "autism spectrum") and are not diagnosed. See my post above for some reasons why the child of a 30- to 40-year-old mother might have a greater chance of being diagnosed than an identical child born to a younger or older mother.
Since we do not know what causes autism, we cannot apply the reasoning under which age is causative for some conditions. For instance, we know that ova tend to degenerate with age, making maternal age a cause of a higher risk of babies with Down Syndrome. We know that tiny, benign colon polyps grow and deform into large, malignant tumors over time; thus, age is a cause of colon cancer diagnoses.
We do not have sufficient knowledge of autism to make any sure statements, in my opinion. The "nerds mating" hypothesis would also explain a correlation of autism diagnoses with older mothers: the highly-educated mother (the bookish sort who didn't have boyfriends in high school) marries the socially-akward IT-guy whose economic value has suddenly skyrocketed. Is their child more likely to be autism-spectrum because of their genes? Is it her age? Is it her (physical) age or her (as it were) life-stage conditions? We don't know.