I think you'll have a hard time finding real data on that specifically. I can tell you just from my experience watching activity on the forums that there is a constant influx of new 'hopefuls' AND a movement in the opposite direction as people give up, get sidetracked, realize they don't, can't or won't put in the work necessary to run a business.
There are a couple of sites that run a yearly survey of the industry and ask questions about how many hours people are working on their business, how much they charge, etc. but that wouldn't necessarily answer your question because it's only the 5 or 600 people who respond on average.
If you search Google for '
small business statistics by industry' you can get some feedback for overarching industries that might contain VAs.
If you do find something that specifically addresses growth rate in the industry please post back, I'd be very curious to know!