I really dislike the amount of effort being expended on discussing the democratic merit of the referendum result.
Direct democracy is not a good way to do things, so whether or not it is democratically acceptable to protest the result or request another one is irrelevant. (Although, of course, the notion that some nervous looking Leave supporters are putting forward, that changing your mind is undemocratic, is clearly ridiculous)
A democratic mandate can not turn a disastrous idea into a good one, and an idea being disastrous does not preclude it from obtaining a democratic mandate. Therefore a democratic mandate can not be assumed to be sufficient justification for implementing an idea unless you feel that upholding democratic ideals is more important than avoiding disaster (which is perfectly admirable, but not exactly pragmatic).