Kenneth G. Wilson (1923). The Columbia Guide to Standard American English. 1993.
fail (v.)
in its transitive use (She failed Spanish; The teacher failed three students in that section) has received criticism in the past, but it is clearly Standard today. When it takes a preposition, fail frequently takes to plus an infinitive: She failed to notice the time. In, at, by, and from are also fairly common: He failed in three successive attempts. We failed at getting them to sign up. We failed by not planning carefully enough. Our company failed from lack of capital. On can also be found in Standard English: The proposal failed on every count.