Unless a significant portion of profits are directed towards the improvement of farming methods, scale tends to decrease quality.
Today there is still difficulty in generating enough incentive to get farmers into arabica, but that changes with different practices, which Blue Bottle has historically practiced (direct trade and direct investment in farms, etc.). This model seems to be very sustainable for the time being.
On the buying end, the roasting end, distribution, etc., the challenges in scaling are similar or the same as scaling any other business as far as I can tell.
My intuition is that consumer demand for genuinely premium coffee would run out before the land or the farmers do, but I know the market far less well than I'm sure others here do.
Certainly we could grow more coffee, and that would likely increase net output of high quality coffee. However, if a company is buying the 'best 10%' of coffee and need to double their output, it is more likely that they buy 80th-90th percentile coffee than reinvest their profits into increase the quality that tranche of coffee to meet that of the top 10%. Even if a company chose to do this, the amount of time it takes to deploy capital in agriculture (~1yr+) is likely much less than the amount of time it takes to deploy capital in manufacturing (months), which effectively would cap growth rate.
Said another way, is the slope of quality distribution that severe?
I'd guess its a long-tailed distribution something like this (https://qph.ec.quoracdn.net/main-qimg-3b21f991d3f0446ce30b9b...) (quality on x axis, volume on y-axis) However, I know little about the complexities of coffee agricultural and manufacturing process, mostly just speaking in abstract armchair economics terms.