Noun form of "extant"?

It seems you are looking for existence.

If you want to emphasize the fact that "just being extant" is in and of itself a main reason for its influence, you could use its mere existence or something of the kind.

Something that would fit that sentence, and your probable meaning since "extant has the connotation not only of 'existing' but more specifically 'still existing'; i.e. it suggests that something has survived over time", is longevity:

long existence or service

Although many similar works were written, none of the others have survived. Its longevity is undoubtedly one of the main reasons for its influence.

Persistence?

The fact of continuing in an opinion or course of action in spite of difficulty or opposition.

The continued or prolonged existence of something.

Oxford Dictionaries http://www.oxforddictionaries.com/definition/english/persistence

Survival is the term of trade.

I would use endurance:

the quality of continuing for a long time

I guess this doesn't necessarily require that the work has endured *all the way to the present day; but that should be obvious from the context of the previous sentence.