t factories (or maybe it was mines) with five times the production cost of their competitors stay in business

For mines, that's very unsurprising: as long as the mineral resources sell for more than production costs it's worth producing. Saudi Arabia produces oil at much lower cost than the marginal well, but it still makes sense to dig new wells. By the same token, small subsistence farmers who have land but can't sell it just earn less than less productive farmers elsewhere.

But you're probably thinking of this post by Robin Hanson, and the 5:1 result is for developing countries undergoing fast catch-up growth (vs 2:1 for developed countries). And it's the worst decile of competitors vs the best, not the worst vs the average.

If you imagine that a 25% cost advantage would let your firm quickly displace all rivals, think again. Yes more efficient firms and plants eventually displace less efficient ones, but it is easy to overestimate the strength and speed of this effect. For example, in a US manufacturing industry with five plants in use, the best plant will typically produce about twice as much with the same inputs (including materials, land, labor, etc.) as the worst plant. In India and China, it will make five times as much: - See more at: http://www.overcomingbias.com/2011/06/selection-is-slow.html#sthash.WfmND8Gj.dpuf

Another robust finding in the literature—virtually invariant to country, time period, or industry—is that higher productivity producers are more likely to survive than their less efficient industry competitors. …

Aggregate productivity growth in the U.S. retail sector is almost exclusively through the exit of less efficient single-store firms and by their replacement with more efficient national chain store affiliates. …

One thing to remember about this is that sometimes lower labor productivity is rational in light of legacy capital investments. E.g. new power plants and factories might require fewer workers, but if you already have the old factory built, you can avoid spending a huge amount of labor building a new factory for a while.