Why do people continue to mine bitcoins independently of their hash rate if their ROI loses 20% every month at the going difficulty rate and the exchange rate BTC/USD is at best flat?
Most miners are speculating that the future value of a bitcoin will be greater than the present value. No profit-oriented miner is happy about the current rate of increase in difficulty. Also, the current rate of difficulty is not a one-way phenomenon. Many factors could cause the difficulty to decrease, such as a flaw that was perceived to be un-fixable. If confidence in bitcoin in general were to drop, mining difficulty would drop as well as mining power and money fled to other virtual currencies.
Other people genuinely want to create an alternate payment network and/or currency and see their contribution in those terms, and not in monetary terms. For those people the price of bitcoins is not their primary motivation.
The answer is, as Nate explained, that the miner is a sunk cost. Obviously, no sane person would buy a miner if they knew they would be in the situation you described.
The future value of Bitcoins is almost irrelevant to the profitability of mining. You can get the same exposure to the profitability of Bitcoins by buying and holding. (The contrary assumption leads to comically absurd results.)
Sane people buy Bitcoin mining hardware because they expect to do better than they would if they used that same money to buy Bitcoins. Changes in difficulty or the cost of electricity may result in them not making money, but no human endeavor is certain to succeed.
As soon as it costs more to provide electricity to the miner than the value of the coins mined, the miner get shut off and retired.
Losing 20% a month? Are you nuts? I bought a miner from KNC last year, the miner arrived a couple of weeks late, but I counted on that. Right now, If I sell my bitcoins as of today's price I would have not only ROI but earned quite a few dollars, not to mention If I would have sold when Bitcoin was at 1000$. Anyway as of today my miner is mining 0.01BTC/day, that is roughly 30cents per month, which equals to 186$. It is still profitable for me to keep mining even if I deduce the electricity bill.
I am one of those that keep his coin in hope of better times, but if I were another kind of guy I would not only have got my investment back, I would have also earnt some nice bucks.