I think there's about a 50/50 chance of either a very successful program, or a phase out, imo.
While there's been a few years now of increased birth rates, there will be a long-term need for more transfers, shorter interbirth intervals, etc., that I don't know yet if we'll see. Plus, we'll need a drastic increase in the number of males breeding- especially amongst Africans.
That said, I think the more likely reasons for a phase out would either be bowing to public pressure or government regulations. While currently I don't think the majority of the public are against elephant captivity, I'm not sure how much longer that'll be the case. AZA zoos need to be very careful as to not have any unfortunate incidents to turn the public perception away from elephants.
Furthermore, while I don't find a nation-wide ban likely, it wouldn't surprise me if certain states or cities moved to ban high-profile species, especially elephants and cetaceans, from zoos. This already occurred in San Francisco, but where else could it happen? I genuinely think it's only a matter of time before Los Angeles Zoo is forced out of elephants due to public pressure, but what other cities or states might follow suit? Again, all it takes is one instance of bad press for legislation to sweep through nationwide.