We report a Monte Carlo simulation study of the phase behavior of colloids coated with long, flexible DNA chains. We find that an important change occurs in the phase diagram when the number of DNAs per colloid is decreased below a critical value. In this case, the triple point disappears and the condensed phase that coexists with the vapor is always liquid. Our simulations thus explain why, in the dilute solutions typically used in experiments, colloids coated with a small number of DNA strands cannot crystallize. We understand this behavior in terms of the discrete nature of DNA binding.