In many popular models of the economy, monetary policy works by exploiting the existence of prices that cannot adjust quickly in response to shocks. If all prices are perfectly flexible so that all markets clear at all points in time, and there are no other problems, then monetary policy has no effect on real variables such as output, and this is true in virtually all reasonable models of the economy.
When prices aren't perfectly flexible, when they adjust sluggishly, inflation can impose costs on some agents in the economy. For example, when wages are fixed, an increase in the price level lowers the purchasing power labor income. The same thing happens to people on fixed incomes, e.g. retirement payments.
But economic agents do not stand by idly while shocks to the price level impose costs on them. Wages can be indexed for inflation, and often have been since the 1970s. Fixed income payments can become unfixed with cost of living adjustments that keep their real values constant. If fixed interest rates on loan contracts are causing unanticipated redistribution of income from lenders to borrowers, then create variable interest rate contracts that move with the inflation rate and offer insurance against this problem. Is committing to prices in catalog's that are printed months in advance a problem? Exploit technology and put the prices online where they can be easily adjusted. Whenever agents experience large costs from inflexible prices, they do what they can to increase their flexibility.
So I wonder if monetary policy will slowly run out of rigidities to exploit as, one by one, agents who have been hurt by price rigidities use technology or other means to to overcome them (and this is also true for other types of market imperfections, e.g. incomplete information).
Should we worry that monetary policy may lose effectiveness over time? Not if our models are correct. In fact, this would be desirable. If all prices are perfectly flexible, markets will behave optimally on their own and there would be no need for the Fed to intervene to stabilize the economy. Presumably, there would also be less chance for error when entire markets rather than a vote of twelve people determines the course of the economy.
Of course, as the current crisis shows, price rigidities aren't the only possible problem the economy can have, so there would still be a role for the Fed to play, but I do wonder if the power of monetary policy to impact the economy will diminish over time.