That's a very interesting topic. I think the following references might be helpful:
Tichenor, D. J., & Harris, R. A. (2005). The development of interest group politics in America: Beyond the conceits of modern times. Annual Review of Political Science, 8, 251-270.
Fisker, H. M. (2015). Dead or Alive? Explaining the Long-Term Survival Chances of Interest Groups. West European Politics, 38(3), 709-729.
Halpin, D., & Jordan, A. G. (2012). The scale of interest organization in democratic politics : data and research methods. New York: Palgrave Macmillan. (in particular chapters 2-4-7)
I second the above. Lowery, Berkhout, and Wonka have -- among others -- published very interesting research on these questions.
Berkhout J (2010) Political activities of interest organizations: conflicting interests, converging strategies. University of Leiden, Leiden.
Berkhout J and Lowery D (2008) Counting organized interests in the European Union: a comparison of data sources. Journal of European Public Policy 15(4): 489-513.
Wonka A, Baumgartner F R, Mahoney C and Berkhout J (2010) Measuring the Size and Scope of the EU Interest Group Population. European Union Politics 11(3): 463-476.
Messer A, Berkhout J and Lowery D (2011) The Density of the EU Interest System: A Test of the ESA Model. British Journal of Political Science 41(01): 161-190.
Beyers, J., Eising, R., & Maloney, W. A. (2013). Interest group politics in Europe: lessons from EU studies and comparative politics. Routledge.
Beyers, J., & Braun, C. (2014). Ties that count: explaining interest group access to policymakers. Journal of Public Policy, 34(01), 93-121.
LaPira, T., Thomas, H. F., & Baumgartner, F. (2012). The two worlds of lobbying: the core-periphery structure of the interest group system. Available at SSRN 2245065.
Hojnacki, M., Kimball, D. C., Baumgartner, F. R., Berry, J. M., & Leech, B. L. (2012). Studying organizational advocacy and influence: Reexamining interest group research. Annual Review of Political Science, 15, 379-399.
Greenwood, J. (2011). Interest representation in the European Union. Palgrave Macmillan.
Klüver, H. (2013). Lobbying in the European Union: interest groups, lobbying coalitions, and policy change. Oxford University Press.
Coen, D., & Katsaitis, A. (2013). Chameleon pluralism in the EU: an empirical study of the European Commission interest group density and diversity across policy domains. Journal of European Public Policy, 20(8), 1104-1119.
Berkhout, J., & Lowery, D. (2010). The changing demography of the EU interest system since 1990. European Union Politics, 11(3), 447-461.
Klüver, H. (2011). The contextual nature of lobbying: Explaining lobbying success in the European Union. European Union Politics, 1465116511413163.
Klüver, H., Mahoney, C., & Opper, M. (2015). Framing in context: how interest groups employ framing to lobby the European Commission. Journal of European Public Policy, 22(4), 481-498.
Giger, N., & Klüver, H. (2015). Voting Against Your Constituents? How Lobbying Affects Representation. American Journal of Political Science.
Berkhout, J., Carroll, B. J., Braun, C., Chalmers, A. W., Destrooper, T., Lowery, D., ... & Rasmussen, A. (2015). Interest organizations across economic sectors: explaining interest group density in the European Union. Journal of European Public Policy, 22(4), 462-480.
De Bruycker, I., & Beyers, J. (2015). Balanced or biased? Interest groups and legislative lobbying in the European news media. Political Communication, (ahead-of-print), 1-22.
Beyers, J., Dür, A., Marshall, D., & Wonka, A. (2014). Policy-centred sampling in interest group research: Lessons from the INTEREURO project. Interest Groups & Advocacy, 3(2), 160-173.
Binderkrantz, A. S., Christiansen, P. M., & Pedersen, H. H. (2015). Interest group access to the bureaucracy, parliament, and the media. Governance, 28(1), 95-112.
Chalmers, A. W., & Shotton, P. A. (2015). Changing the Face of Advocacy? Explaining Interest Organizations’ Use of Social Media Strategies. Political Communication, 1-18.
Tatham, M. (2015). Regional Voices in the European Union: Subnational Influence in Multilevel Politics. International Studies Quarterly.
Weiler, F., & Brändli, M. (2015). Inside versus outside lobbying: How the institutional framework shapes the lobbying behaviour of interest groups. European Journal of Political Research, 54(4), 745-766.
Pedersen, M. J. (2015). Neglecting results? A critical view of the literature on organised interests in the European Union. Journal of Public Affairs.