I decided to start with the sororities because there was fewer orgs and that their reasons for no longer existing were much more cut and dried than that of the fraternities.
Of the 18 orgs:
3 died out being too weak to sustain themselves (it is unsure if 2 of those orgs dissolved or merged with another org).
10 merged with an NPC org
4 merged with an org that later merged with an NPC org
1 was renamed due to a merger with another org which subsequently merged with a third org that later merged with an NPC org.
The oldest and largest org that merged was Beta Sigma Omicron, which existed 75 years and had 61 chapters. The second largest org was Pi Kappa Sigma, which existed 64 years and had 48 chapters. Neither org acquired their chapters from mergers.
Sadly, however, BSO only had 15 active chapters at the time of the merger. It is unknown how many were active with PKS.
Perhaps if we knew for all orgs how many active chapters there were at the time of the merger, it would help us to reach a more definitive conclusion on the strength of their orgs and possibly why they merged.
ETA: OMG, there is already a GC thread on this very subject that I briefly perused, then forgot all about it. I'm still glad I did my own research, I think a got a little more meat in my data that helped me with my research:
GC Thread: NPC Orgs That Didn't Make It
Threaded Mode