Many a small business(此作小商店) has failed because of lack of i

意思是“不止一个”
相当于“more than one”
虽然意义上是复数,但在语法规定上谓语动词仍用单数
在这一点上“more than one”的用法也是一样的
如：
Many a man has tried it before.过去试过的不止一个人了
More then one person is involved in the case.涉案的不止一个人.
如果还是不清楚,可以到语法书主谓一致专题上找.