Airbnb is working on pulling out all the stops to try and prevent layoffs. They might not succeed, but if they were a smaller company they wouldn't even have anything to try.

Is there anything inherent in their size which means they can weather the storm?

I think big isn't just pure size. Groupon was a 'big' company in chicago with ~10k employees here.

Company size is positively but not perfectly correlated with stability.