I'm not quite sure, whether I understand the focus of your question correctly, because I don't know your special research background.
At first, I assume basically, that sustainability can be attained in social housing estate. I've done an international study (in German) about the living conditions of elderly homeless men in industrialised western countries. Countries with little social housing estates, like USA, Canada and Australia, have got higher rates of homelessness, compared to countries with large social housing estates, like UK and Germany.
In order to provide affordable housing for poor people, in my opinion, you need social housing estates. You can regard social housing as a soco-political intervention in order to combat housing inequality.
(Second idea) In spite of that, you can argue, that there are many definitions and assessment toolkits, in order to measure the sustainability of social housing estates. If this is your focus, I recommend, that you either develop an own general definition or use a general definition. Perhaps you find a practical definition on the website of UN-HABITAT (United Nations Human Settlements Programme); see link below. In addition there's much material / literature about social housing; for example: (see links)
Planning and Design for Sustainable Urban Mobility. Global Report on Human Settlements 2013
Planning and Design for Sustainable Urban Mobility:Global Report on Human Settlements 2013 – Policy directions
If you google on the UN-Habitat website the term "social housing" (see below), you can find about 15 documents, analyzing and reporting worldwide about social housing.
(Third and last idea) Perhaps your focus consists of thinking, the sustainability of social housing estates can not be measured, because there are so many definitions and assessment toolkits used, that the various reports, studies or analyses can't be compared against one another. In this case, I recommend to use an general and practical definition of social housing in order to filter out relevant data for your research. (Maybe you can get datasets from the UN.)
If you pursue another research aim, let me know, perhaps I can supply some detailed information about this.
Good luck and kind regards
DetlefPS: There are some reports / studies, maybe you are interested (see files below):Gurran et al (2008): New directions in planning for affordable housing: Australian and
international evidence and implications.
Alan Morris et al (2012): Is social mixing of tenures a solution for public housing estates? (Evidence Base, issue 1, 2012, journal.anzsog.edu.au, ISSN 1838-9422)
Adams Integra (Ed) (2009): Affordable Housing Economic Viability Study. Report for the consideration of Salisbury District CouncilPawson et al (2011): Social housing strategies, financing mechanisms and outcomes: an international review and update.Fitzpatrick, Stephens (2007): An International Review of Homelessness and Social Housing Policy.
I would like just to add a brief comment regarding the word "sustainability", once it is not a scientific concept (as gravity is, for instance) but a political value/principle such as justice and freedom. That is why there are so many "social and political" meanings related to it, which leads to the 500 definitions of "sustainability in social housing estates", as you mentioned.
You can have a general access to a brief history of the origins of the word here: http://bibliothek.wzb.eu/pdf/2007/p07-002.pdf
The author, Ulrich Grober, affirms that the history of the word's meaning goes back to the XVII Century and is related to a set of rules in the public administration of forests. Very interesting and intriguing.
Another document that points out to this definition problem is the map created by Amir Djalali and Piet Vollaard: The Complex History of Sustainability. You can check it here:
I have been thinking on this topic of sustainabilty for quitw some time now, In this I must admit my thinking and reading has started to sway. My position at first was leaning to the possibility of having some social program like the one you refer to be sustained. Howerever, living in the U.S for almost 55 years I am becoming more and more sceptical as time goes goes on. From my perspective based in Critical Social Theory, I asked myself and request all to ask ouselves; what has human kind socially built, excluding bricks and morter, that have been sustained? In thinking and searhing on this question I find less than the fingers on one hand.
That is were I would start Paulinus. It does not matter what others have defined, it is how you define it. Just as you can reject or think about what this responce is refering to. For example, when you think about sustainability does it include time and space? If it does then you have another starting point. Second, is your thinking on sustainability focused on communnity,state, nation state, or global? Third, what is the context in which you define sustsainabilty, this will greatly narrow and focuse the research. Fourth, as you research; ask youself what is connecting all the various studies together? Think about presuppositions, philosophicy, theory, political influence. I hope I don't sound as if... Fifth, consider what is burried deep in the relationship between this question the related research. Finaly, what I believe to the most important and rearly mentioned in discussions on research is look for what is not there (relates to 4) not said not reported. A lot of times silence and absence speak.
Last, my amswer to the first paragraph's ending question has something to do with linear time, not space in the geographic sense, and are global. Three concepts have meet my definenetion of sustainabilty, the first being patrairarchy and the others I leave to you Paulinus and others.