This is likely too modern of an era to really be discussed here, so I'm wary of getting into it, and would suggest /r/geopolitics as perhaps a better (albeit less strictly moderated) forum for it. That said, I'll try my best to avoid a post-1996 discussion, but I'll state outright I would argue that the 1998 global recession, which particularly hurt Russia, was a major factor in this.

Anyways, with the Soviet Union over at the start of 1992, and Russia effectively replacing it, NATO was left to find a new way to stay relevant. There were overtures for Russia to even join NATO, but I seriously doubt the seriousness of that, and would think it nothing more than political grandstanding on either side. However several former Warsaw Pact states did express a desire to join the organisation, including former Soviet states (though again, this is treading into modern territory).

However Russia faced a lot of issues: political, economic, territorial, and so on. Yeltsin was busy trying to establish a market economy in a region that had been centrally planned for 70 years, and the results were not going well. Add in issues like the Chechen conflict, his own political survival against a still-popular Communist Party, and trying to establish democracy for the first time in Russia, and NATO-Russia relations were not a priority. While I think that both sides would have liked to develop closer ties, there was just far too much going on internally in Russia for them to seriously consider the prospects, and then with the collapse of economy in 1998, downfall of Yeltsin and rise of Putin and subsequent strengthening of the economy (all of which I'm not getting into detail here), it became a moot point.

So in short, unfortunately it's really too modern of an issue to really get into here, though the early stages of the problems due stem, I'd argue, from the general chaos of the end of the Soviet Union and trying to establish order in post-Communist Russia.