A woman can not have communion while having her period because she is bleeding - not because she is unclean. I wouldn't be able to have communion if I was bleeding either. It is just one of those things - and it is good for teaching us humility - we can't always have what we want when we want. It is a big deal to take the Living God into one's own body, not something to be taken lightly without due preparation.
(Don't worry Bluetoria, I know you respect me, and Orthodoxy, it is just an area we'll have to agree to disagree about. If I was female, I don't know how hard or easy it would be for me to accept these rules, but there has been occasion when I have been unable to Commune, even though I'd prepared, and it made me realise that while I thought I was ready for Communion, spiritually I wasn't prepared at all, and so God saw to it that I would be unable to Commune that day.)