Abstaining from an object in Latin can leave you with one of three grammatical constructions, given here in the order of frequency:
- abstinēre aliquid/sē + ablative of object
- abstinēre aliquid/sē (absolute)
- absintēre aliquid/sē + genitive of object (cf. Greek ἀπεχἐσθαι τινός)
Here some examples of how and from what the Romans refrained—
- virgō nuptā abstinet — virgins abstain from marriage
- vir sapit quī urbis rēbus abstineat — the wise man holds off from politics
- mē ostreīs et muraenīs facile abstinēbam — I easily abstained from oysters and eels — Cicero, Ad Familiārēs 7.26 (they make him nauseated)
- mihi abstinē invidere! — don’t bother pitying me!
- animum coluit abstinentem pecūniae — she cherished a frugal mind
Latin for Addicts 
Good to know. It seems that Latin speakers often weren’t always quite sure which case construction was most appropriate. I’m reading Hugh of St. Victor’s De grammatica, which includes a chapter on ambiguous case constructions, a chapter mostly borrowed from Priscian.
I have a question on your final example. If you’re using coluit as a transitive, shouldn’t the object be the accusative “animum”? Thus, “Animum coluit abstinentem pecuniae.” Or, in the less likely case that “coluit” here is from the intransitive “colescere,” the sentence as you wrote it could mean, “The mind grows strong as it keeps far from money.”
You’ve hit on a weird mental gymnastic I did in the draft, where I wanted to make a general statement as w/ your second example, but then decided that I should have a female subject for one of the sentences so I switched it at the last minute. Good catch.