I’m trying to think of industries that provide goods or services which are still in demand, and will be in the future, but where improved efficiency in the production process (etc.) has caused the number of producers to fall, or the size of the producers to decrease. That is, the growth in efficiency has grown more than demand and, since that’ll drive down prices, either some producers have to leave the market, or the producers have to scale back operations.
Can anybody think of any examples?
All of 'em, eventually. How many silversmiths does your town keep busy? 
To give a few other examples:
The automotive industry has historically trended towards consolidation. While Japanese and Korean industries have entered the world market, smaller manufacturers have fallen by the wayside (i.e., Studebaker, M.G.) or been absorbed by larger firms (i.e., Jaguar, now part of Ford.) Even most of the big companies have partnered with other companies.
Five to ten years ago, US dairiy supply far exceeded demand. Then, bovine growth hormone was introduced, further increasing supply and changing the industry from a barely-break-even proposition into a losing one.
Equipment costs in the semiconductor industry increase at an almost exponential rate. It is possible that in the future only a few large foundries will be able to foot the bill for r&d and to build new fabs.
Farming.