I think, to be honest, there are times and auditions when it's acceptable to make another attempt at things, and times when it isn't - because, occasionally, we do make far more of a hash of things and we know we can do better - but you should be empathetic enough as an actor to judge those in the audition room.
Certain types of audition are far more amenable to you taking your time and exploring material several different ways, anyway - many theatre auditioners are not in a particular hurry to see you deliver, and happily spend upwards of fifteen or twenty minutes with you, on occasion, seeing you interpret material several different ways. They are often keen to see you show imagination and versatility by trying different things. They are partly looking for those who will gel well with others in the rehearsal room, listen to direction, and prove themselves able to explore a wide range of possible options within a rehearsal period, long before anything is set in stone.
Screen casters tend to want to see more solid, decisive delivery from the word go (because there is no time in screen terms for actors who can't make good choices on set and make them count with minimum rehearsal), but I agree with Mark: there is no screen director worth his/her salt who feels that one take is all that's needed to elicit a fine performance. Therefore, if you slip or misdeliver in a screen test, you should behave just as if you were on set, and ask, profesionally, if you can pick up or start over. Most will accede to this, because it's what is done on the set. I am not so convinced that you should ask if you can do the whole thing over again *once you've finished*, as that would just waste time, but while you are still engaged in the moment, sure.
For commercials, though, I honestly think decisions are made as soon as you walk through the door, you do what is asked of you, good or bad, and you let it go. 9 times out of 10 you don't book the commercial unless you are *exactly* the type that is being looked for, anyway, and I have never known *any* commercials casting that took longer than five minutes at the initial stage of casting. In the world of commercials, time is money and they make casting decisions at the drop of a hat. It's perhaps interesting that the casting director initiated the request as to whether you should perform the piece again (as, often, they wouldn't bother to do that), but it's impossible to know the motive: it could, very likely, simply have been intended as a courtesy question addressed to the director, and, in that sense, this conversation would have been considered 'none of your business', anyway: The CD asked the director a question in order to help the director (and/or make the CD look more efficient), the director dismissed the need to see anything further, and that, I'm afraid, is that. The point I would always maintain, however, is that, asking to do something again when no-one has confirmed/denied whether they would accept that or otherwise, but *you* feel you would like to have another go, is one thing (they can only politely dissuade you or take you up on it), but pushing your case when someone in charge has definitively said 'no' to seeing more is quite another. Do not do it - it will only ever be seen as you trying to square up to the director and suggesting you know better than them, regardless of how honourable your motives might be.
