I'm just guessing here, but it seems to me like offering the exact same offer over and over several times in a row would kill the swap. There's a limit to how many people would want those eggs, so pretty quick, nobody will take the offer. It would be more polite to wait awhile between claiming offers if all you have to exchange is one breed.
The egg swap chains are pretty delicate to keep going, as it is. I don't think it is an objection to one person claiming lots of eggs. it is more an objection to the rest of the participants seeing nothing but the same offer, over and over.