Solution 1:

I believe that all verbs that end in -ide (/aɪd/) regularly produce adjectives ending in -isive (/aɪsɪv/) where the diphthong is preserved.

  • cicatrisive
  • collisive
  • decisive
  • derisive
  • divisive
  • incisive
  • indecisive
  • precisive
  • previsive
  • subdivisive
  • subrisive
  • undecisive

In contrast, verbs ending in -mit /mɪt/ regularly produce adjectives ending in -issive /mɪsɪv/, with a double s to keep the i vowel “short”.

  • admissive
  • commissive
  • dismissive
  • emissive
  • fissive
  • insubmissive
  • intermissive
  • intromissive
  • irremissive
  • manumissive
  • missive
  • omissive
  • permissive
  • photoemissive
  • promissive
  • remissive
  • retransmissive
  • submissive
  • transmissive
  • unsubmissive

Both the OED and the OALD agree with this.

I’m thinking therefore that the “other” pronunciation is less broadly accepted, perhaps a regionalism or sort of hypercorrection due to interference with divisible /dɪˈvɪzɪbəl/.

It certainly sounds odd to my own ear.

Solution 2:

The dictionaries disagree, so they must be both right!

Actually, I've heard four pronunciations; /dɪˈvaɪ.sɪv/, /dɪˈvɪ.sɪv/, /dɪˈvaɪ.zɪv/ & /dɪˈvɪ.zɪv/,

Solution 3:

There's actually a lot of interesting information in other places on the web about this topic, so I thought I'd post an answer summarizing some of it.

Apparently, /dɪˈvɪsɪv/ ("divissive") is more common in Canada

According to the post "The great divide" by Katherine Barber on her blog Wordlady,

At the Canadian Oxford Dictionary we found that "di VISS iv" is in fact the most common pronunciation in Canada for this word.

This preference for "di VISS iv" seems to be unique to Canada. Dictionaries from other countries give their pronunciations of the middle syllable in order of frequency:

Britain: VICE
NZ and Australia: VICE , VIZZ

US: VICE, VISS, VIZE, VIZZ
Canada: VISS, VICE, VIZZ, VIZE

The pronunciation "divissive" is uncommon in British English

Ben Yagoda's blog Not One-Off Britishisms also has a post about this pronunciation.

There has been a fair amount of grumbling about Obama and various members of the chattering classes using the “divissive” pronunciation, much of which assumes they are aping the British. That is understandable, given the way the Brits say “vittamin” and “dinnasty,” but it is not correct. The OED lists only one pronunciation for the word: with a long i. A lengthy discussion at the Washington Monthly website (which descends to personal invective at the end in a predictable, almost ritualistic manner) suggests the short-i is an American regionalism, found in New England and the Midwest. (Apparently former South Dakota Senator Tom Daschle said it that way.)

There are some interesting comments that seem to support the above generalizations in this Straight Dope thread, "How do YOU believe the word "divisive" is correctly pronounced?"

05-22-2012, 08:21 AM FloatyGimpy
I'm Canadian, I've never heard it pronounced with the "eye" sound.
[...]
05-22-2012, 04:56 PM Teacake
British. Div-EYE-sieve. I've never heard it pronounced the other way.

Solution 4:

Comparing divisive to division is confusing the issue. Those who divide are divisive, those who decide are decisive, etc. Long i" sounds. We don't say, incissive because of incisions, for example. It's incisive for incising.