Innovation in specific areas slows or stops all the time. The general run of technical progress in a specific area shows an S-curve, in which initial discoveries are made slowly, later progress accelerates as synergies are exploited and greater investment is made, and finally innovation decreases as low-hanging fruit is exhausted and the shape of available technology matches that of the problem domain. For an example of this, see aerospace; it took around sixty years to go from the field's inception to the moon landing and the Concorde, and in the fifty years since we've made mostly incremental progress over the technologies involved in both.

It seems that we're currently approaching the top of the S-curve for computation via integrated circuits; further increases going forward are likely to be incremental and margin-focused, as opposed to paradigm-shattering. Maintaining the 1950-2010 rate of productivity improvement will require new paradigm-shattering advances in some other field (machine learning? Internet of Things stuff?). It's possible that these are indeed forthcoming, and we can continue our absurd growth levels for another fifty years. It's also possible that we're nearing the edge of the problem space and we won't have any more easy order-of-magnitude productivity boosts. If the latter is true, then our economy will inevitably collapse with enormous collateral damage. As an economic system, this seems unstable at best.