Learn English – Which preposition follows “persist”

Intention is a Nominalization derived normally from the verb intend plus the nominalizing suffix -tion. As with many nominalizations, it forms a periphrastic idiom for intend: have D intention where D is some Determiner, like an, any, no, some, the, etc.

Also as with many nominalizations from predicates, constructions used with the predicate can be used with periphrastic constructions made from the derived noun, like Equi Infinitive Complements, for mental predicates.

• He doesn't intend to kill his gecko. ~ He has no intention to kill his gecko.
• He is not inclined to mow his lawn. ~ He has no inclination to mow his lawn.

In addition, the noun intention can take a gerund complement describing the content of what the subject intends. Naturally, a preposition is required to link the noun with the gerund, and since the gerund describes the content of the mental state, it uses the common possessive of.

• He has no intention of killing his gecko.

This is a fact about intention, however; other nouns (derived or not) may or may not allow this construction (in fact, they likely won't, because this kind of individual constraint helps distinguish predicates). Thus, the following are ungrammatical:

• *He has no inclination of killing his gecko.
• *He has no desire of killing his gecko.
• *He has no plan of killing his gecko.

I thought I would update this with the result of the poll that the original poster ran, so that future visitors to this site can see them no matter what happens to the linked site:

The following comment by BoldBen may also be valuable; it had one upvote at the time this answer post was made:

I've just voted for 'about' in the poll only to find myself in the minority. I would say 'What do you see as the difficulties with adopting' but not 'What concerns do you have with adopting'. I wonder whether 'concerns ... with' is more common in the US and concerns...about' more common in the UK. There is also the form 'concerns...regarding' which is certainly used in the UK; I don't know whether it's used in the US or not. – BoldBen Nov 16 '16 at 9:25