I don't know anything about LW's internals, but in most sane architectures you'd want to have a last-downvote timestamp linked to each user's account, and to compare the timing of incoming downvotes against it. If the difference is too small, you reject the input and display a message similar to the one you get when you're about to post in a heavily downvoted thread. That message has a few issues -- it doesn't come up if the vote total upthread dropped below the threshold between when the page was loaded and when the post was submitted -- but since we only care about session-local behavior here, that shouldn't be a problem. Synchronization between the session and server time might be harder but that depends on details I don't know.

I can see a behavioral pitfall, though. I typically decide on votes after reading through a screen's worth or so of a thread, and this sometimes implies two or more downvotes (for example in the cases of short low-quality posts or discussions inappropriate for the site). I'd find it gratingly aversive to be forced to wait N seconds or minutes between posts in these cases; I don't know if this happens often enough to outweigh the mass-downvoting problem, though.