Well, considering the fact that "heritability" is a measure of how much of a given phenotype's expression is due to genetic variation, probably not soon. "Heritable" is not a word used to refer to environmental factors such as parental care and upbringing. In studies on heritability of specific traits, these environmental factors are used as classifications for broader observations of genetic variations (for example, in twin studies, was twin pair A raised in the same household like pair B?).
Going back to autism specifically, the Simons Foundation Autism Research Initiative identified a single genetic mutation that accounted for 25% of diagnoses in their Simplex Collection[1], while the other 75% were impacted by 200-400 different genes. This data is available online as of 2016[2], though some analyses may be paywalled.
[1]: https://sfari.org/resources/autism-cohorts/simons-simplex-co...
[2]: https://www.simonsfoundation.org/features/foundation-news/si...
http://www.npr.org/sections/health-shots/2015/09/02/43674237...
(Audio controls in the left margin.)
He addresses that a fair bit, mentioning that autism is one of the most heritable conditions, and talking a lot about the history of the diagnosis and how it was artificially narrow for a long time.
Personally, my bet is that we'll come to see a lot of autism diagnosis as part of a broader pattern of medicalization of deviance from the norm. And that even the forms we eventually decide are harmful have for nerds the same relationship that sickle-cell anemia does to malaria resistance: a trait that is useful in small doses but can be harmful in large ones.
If there is an actual increase, I'd bet on it being due to stronger assortative mating that has come as mate choice has less to do with geographic factors and more with education and workplace.