Politics in the US right now is neither particularly rational nor strategic. Regardless of anything that happens in Russia, we should expect that unless the situation in the US Congress changes, Jackson-Vanik will live on.
As is well known, the Jackson-Vanik amendment is outdated. It was intended to address the issue of restrictions on Jewish emigration from the Soviet Union in the 1970s by denying "most favored nation" status to the USSR and other communist countries that restricted Jewish emigration. The amendment was added to Title IV of the 1974 US. Trade Act and remains in force today, although the President of the US can grant a yearly waiver. It is not possible for the law today to serve its original purpose because the USSR no longer exists, and Jewish emigration is no longer subject to the restrictions that inspired the law. It would seem obvious then that the law should be repealed. Indeed with the "reset" of US-Russian relations by the Obama administration and the call for the repeal of the law by Vice President Joseph Biden in March 2011, it seemed like repeal was imminent, but so far nothing has changed. Upon closer inspection, the failure to repeal Jackson-Vanik should come as no surprise.
Over the years, Jackson-Vanik has come to be viewed as an inexhaustible source of leverage against Russia, a bargaining chip to be forever promised but never actually cashed in. Whenever someone wants Russia to do something, the law is held up as a quid pro quo, where if Russia were to do X, then Jackson-Vanik would be repealed. Despite whatever is done on the Soviet or Russian side, however, the law is mysteriously never repealed. The most obvious case for its repeal came when Mikhail Gorbachev lifted restrictions on Jewish emmigration during the late 1980s; the end of the USSR in 1991 was another prime moment for repeal. In the 1990s, Jackson-Vanik was repeatedly held up as a bargaining chip.
At this point it is safe to say that Jackson-Vanik no longer can be connected to any real situation on the ground in Russia. For this reason it is a mistake to look to something that is actually happening in Russia in order to understand the law's persistence. It does not matter if Putin becomes President of Russia again in 2012. The repeal of Jackson-Vanik will be a function of US politics, not Russian policy or politics.
Politics in the US right now, however, is neither particularly rational nor strategic. The Congress is beset by bitter partisan gridlock, where success is no longer measured in terms of any positive legislative achievements. The bar has sunk so low that merely passing a continuing resolution to keep the government from entirely shutting down is a major legislative victory. In this environment who is thinking long term? Who is asking whether laws make sense, or whether they serve their intended purposes?
The answer is that while there are some dedicated, intelligent, and competent members of the US Congress, the institution as a whole is not functioning particularly well at present, and it is a mistake therefore to expect that the US Congress will pass or repeal laws on the basis of a law's strategic value (e.g. Jackson-Vanik's role in US-Russia relations). In addition, beyond the US Congress, President Obama has other more pressing matters to attend to, including a recession, an election, and the specter of a catastrophic failure in congressional approval of budget appropriations this fall. Taking the US political landscape into account, we can conclude that regardless of the merits of repealing Jackson-Vanik, and regardless of anything that happens in Russia, we should expect that unless the situation in the US Congress changes, Jackson-Vanik will live on.