Verb + infinitive, no preposition
faillir
no preposition
The constructions
no prepositionfaillir + infinitif
J'ai failli tomber.
Do not writeJ'ai failli de tomber.
Why
Faillir followed by an infinitive means you very nearly did something, and takes no preposition. It is almost always used in the passé composé: j'ai failli rater mon train. Manquer de, with de, means the same.