I don't think the browser matters, I use firefox and I disconnect a lot, and it's the same way--in waves--some times there's times where it doesn't disconnect and its doing good, but other times it disconnects me every single match either in the beginning or halfway, so I can't pvp most of the time.
Also there's times when even if I'm not disconnecting, then I desync and lose that way too, and this also happens in waves, which seem to be occurring more frequently for me. And no, I do not have multiple tabs/windows open when I'm playing.