Will the amount of "usable" Bitcoins eventually drop to zero? Let's assume that there is a non-zero probability that people lose their bitcoins, e.g. by forgetting their password. The amount of bitcoins these people possess will become "unusable" but still remain in the blockchain and contribute to the maximum quantity of 21.000.000 bitcoins. 

Over time the amount of "usable" bitcoins would shrink more and more as people keep losing bitcoins. Will the amount of "usable" bitcoins eventually approach zero? What will happen then? Is there a mechanism to somehow recover lost bitcoins? At the moment I don't see such mechanism.
Lost bitcoin are protected by the same security that protects bitcoin in circulation or storage, hence lost coins are lost forever.

There are many ways of looking at this "dilemma", and its effects are different depending on the economic context, but coin loss/destruction is generally considered to contribute to the value of the remaining "usable" coinbase. Since the lost coins are permanently removed from circulation and become unusuable, the principle of Supply and Demand implies that the remaining usable coins will become more valuable.

In economics, this process is called deflation of money supply. It has the effect of increasing the value of each token. It is the opposite of inflation of money supply ("money printing"/quantitative easing) where additional tokens are created with the effect that each token's value is decreased as the pool of tokens grows in relation to available goods and services in the economy.

You might be interested in this detailed discussion: Inflation, Deflation, Money and Credit