Said Armstrong did take 13 years to fall though, in which time the sport gained a lot of traction. At that point in time though, after Festina and Pantani, what would another positive REALLY have done? The public esteem for cycling couldn't have fallen much further, and it would have rebuilt around Ullrich instead, which would have led to the same period of tempest from 2006-7, just with a slightly different implication.
So you just get a fall in the number of big global companies and a rise in the number of smaller, local companies. FDJ, or Lotto, or Cofidis, or Euskaltel, or Lampre, are hardly big multinationals. They get exposure in their home market and support from home fans, and that's all they need to make it worth it. Why should FDJ or Euskaltel care if Bradley Wiggins tests positive, as long as the French and Spanish TV channels are still showing it? The sport's too ingrained in their home market to die out entirely, so they'll be fine. Cofidis have stuck with it through thick and thin. Hell, what will it take for LA Aluminios to give up on the sport? Cycling offers comparatively cheap sponsorship, and at a much greater level than in other sports for the most part (jerseys emblazoned with your logo, commentators mentioning the trade team names every five seconds), and if the sport's stock falls, that will only make it cheaper.
The races are more of a worry than the teams, but frankly the main problem for the races is the economy rather than sponsor willinghood to fork out for a sport known for doping. Liberty Seguros might not sponsor a team anymore, but they do sponsor the Portuguese national squad and pretty much every extant race in Portugal gets some sponsorship money from them. Cycling at all but the top level is reliant on fans in businesses and similar, and that won't change, just might invade the top level a bit more than usual.
It's teams without a focused identity like HTC, or teams that are directly embroiled in the scandal, like Rabobank, that are vulnerable.