Of course there have been many questions raised about the tendency for falling rate of profit. But doesn't one have to be clear about what one is criticizing? From the very beginning (e.g. Capital, Vol 3) proposition has been this "tendancy" in the context of the so-called "countervailing tendancies" (CVTs). Its a "tendancy" and not the final word. One big CVT: at some point when the profit rate got too low, a depression would ensue and the price of capital would fall enough to start the cycle all over again. [Other CVTs include: improvements in technology that would lower the cost (labor time) put into machinery and material inputs; or technology improvements that would lower the cost of hiring labor (cheaper clothing, food, etc).]
So, what has been proposed is a theory of long waves\cycles etc. - periods of ups and periods of downs in the profit rate over decades (with lots of short run fluctuations within the long ones). This serves as a context within which political and class struggles then play out - and IF this is true, it is strategically very important information for those struggles. MAYBE the falling proposition of a tendancy for a falling rate of profit is (or is not) relevant to relationships with the 3rd world. But what has NOT been proposed is a steady unending decline in the rate of profit that should have gotten to zero by now (never mind some automatic collapse of the 'system'). [Admittedly, some interpretations of Ricardo, but not Marx, would lend themselves to your statement.]
Now there are lots of things to querry about the proposition of a falling rate of profit. As John points out, many people have questioned the explanatory value of calling one thing a 'tendency' and something else a 'countervailing' tendency when both are 'built in' and operating all the time. And why assume the CVTs involving technological improvement will not be larger than the "main" tendancy? To me this is a debate about the 'explanatory value' of a concept that explains how things work themselves out - and therefore should not be a matter of political principle. In good part, it should hinge on whether they help illuminate the historical "facts"- do these waves actually happen and for the reasons proposed? But we have very, very little "data" (estimate today's capital stock; estimate it for 1860) and only a handful of people have done work on this, so there is LOTS to think about.
Paul