Rolling again, is no weakness at all. The next roll is also random and exactly as unguessable as the first. If the game was done 'without replacement' then the field would be reduced, but it isn't, and the field is unimaginably huge anyway. There is no effect whatsoever by 'rolling again' until you are happy with the result.

My buddy Tom always generates UUIDs by hitting the button several times. It gives him pleasure to 'waste' all those random numbers.