There was a Planet Money podcast (or similar) recently that talked about tax cuts to small/medium size businesses. They looked at a few anecdotal cases and small cuts in taxes didn't result in enough money to hire someone or spend large amounts. They just simply weren't paying a ton in tax anyways, so a cut here or there wasn't a big change.
I could ask a similar question, how many businesses would fail with a 0% tax rate. If we reduced that barrier to entry, more people would open businesses, thus creating a ton of competition, which would lead businesses to fail.
Businesses are going to fail no matter what. Sometimes it's the tax rate, sometimes it's the market, the location, the product, the employees, the manager, the owner etc etc etc.