Leaking faucet in bathroom sink

Pretty much what I show in the diagram. One of the handles, if it's not turned exactly to 90˚, causes the faucet to leak. And sometimes even when it's at 90˚ I have to fiddle with it a bit to get the leak to stop. (The kids, of course, never bother to fiddle with it, so I often find the sink has been leaking for hours since the last person used it.)

It seems like it shouldn't be possible to turn it past 90˚, so presumably something is loose. Is there a way to tighten it? Is that not the...

Leaking faucet in bathroom sink