Even if they were derived from the same root in Latin, they came to English by different paths, migrating whatever suffixes they had into root somewhere along the way.
I'd speculate Miniature is probably a root by itself. I'd speculate that minimum, minimal, minimize have common root minim (or maybe minimum with possible dropping of um part to accommodate suffixes -ize and -al). minor and minority same way have common root minor; and minus and minute are roots by themselves.
Interesting question with an interesting answer. I understand what @subic is trying to get at. Taken from Dictionary.com, here is the etymology of "absent":
1350–1400; Middle English < Latin absent- (stem of absēns, present participle of abesse to be away ( ab- ab- + -s- be ( see is) + -ent- -ent))
@subic, were you wondering over the 's'? Well, I looked up further, and I realised why the 's' was there at all. From Wiktionary:
From Middle French absent < Old French ausent < Latin absent-, the stem of absens, present participle of abesse (“to be away from”), formed from ab + esse (“to be”).
Note that "abesse" as you said was the original word, but the Latin word is "absent-", whose root is "absens". IT was here, that 's' first got stuck in. Why? I looked up the Latin absens, and I got this:
Present active participle of absum (“be away from, absent”)
So, absens came from absum, so I looked up absum, and I found this:
From ab (“from”) + sum (“be”).
The 's' originally came from 'sum', and along with all the deriving and everything, remained there, as it was derived from 'absum'. In fact, if you looked up "abesse", you would find that it is actually a derivative of "absum"!
So, the thing that is confusing, is abesse, which is actually a :
present active infinitive of absum
So, I hope that answered your questions.
Best Answer
It sounds like you've already answered this question for yourself from the etymological point of view.
With regards to modern English, I wouldn't consider the ab- prefix to actually be a productive negative prefix of any kind. In the case of abduct, it's hard to argue that ab- is a negative prefix at all, especially since the stem duct is not obviously related in English to the meaning of abduct. You have to know Latin to make that connection. In the case of abnormal the ab- prefix does attach to an existing word normal, but its meaning here is simple lexical idiosyncracy.
So it is with abortion: I would argue that the stem abort is morphologically simple in English, with the Latinate prefix ab- being an unanalyzable part of the stem from a synchronic point of view. (And most English speakers have never heard of the word ort, and certainly wouldn't connect it in any way to the word abort.)