How can interest rates be so low? Over and over again reputable economists and pundits like Alan Greenspan tell us that the 0% interest rates are "unsustainable", yet they are sustained.

How can interest rates be so low? Throughout all of history I could only find interest rates down to 3%, never lower, yet now we have 0% or even negative interest rates. How is this possible?
There is a demand for debt and a supply of debt. The demand for debt is determined by the extent of profitable investment opportunities that are around. The supply of debt is essentially people's saving multiplied by a factor depending on how much risk financial institutions are willing to carry.

Suppose we live in a world where there are no clearly profitable investment opportunities, but many projects which return the same money you put in on average. So nobody would take on debt at positive interest rates. However, even a a zero interest rate, people would still want to save money, for example to insure against bad times, or for retirement. So there's an equilibrium in which the interest rate is zero, but people still borrow and lend.

Another possibility is that people just expect deflation, so a zero nominal interest rate still goes along with positive real returns on your investment.

It is not clear to me what you mean by sustainable, but clearly such situations can arise, albeit rarely. Japan has nominal rates close to zero for a long time now.