When want to negate a finite clause—a finite clause is a clause in which the main verb has tense—the negative adverb not must appear either after the auxiliary verb, or actually cliticised onto the auxiliary. Some constructions in English, such as the present simple or past simple do not use an auxiliary verb in canonical delcarative sentences:
- Elephants eat donuts.
- The elephants ate the donuts.
Notice that both of these clauses are tensed. Now, if we want to negate these clauses we will need to insert the dummy auxiliary DO, because the word not must come after the auxiliary verb:
- Elephants do not eat donuts
- *Elephants not eat donuts (ungrammatical, no auxiliary)
- The elephants did not eat the donuts.
- *The elephants ate not the donuts (non-standard in modern English)
However, none of this applies to the clause (not) to ask any more in the Original Poster's example. Why not? Well, the answer is that this clause is not a finite clause. It does not have any tense. The verb try is followed by an infinitival construction using the word to followed by the plain form of the verb. The plain form is not tensed. It is neither present nor past tense:
- *She will try to eats all her food.
We can see from the example above that if we use a present tense form of the verb after to, the sentence is ungrammatical.
This clause after the word to is a non-finite clause precisely because it is not tensed. When we negate a non-finite clause in English, we do not need any auxiliary verb. When we are negating a to-infinitival construction, we just put the word not directly behind the word to
- He tried [not to show his surprise].
Here we see the word not appearing before the word to.
We may alternatively put the word not directly before the plain form of the verb:
- He tried [to not show his surprise].
This is less common, but equally grammatical.
Notice that the auxiliary verb DO is always tensed in English. It is barred, therefore, from appearing in non-finite constructions:
- *He tried to didn't show his surprise. (ungrammatical - tensed verb in to-infinitival construction)