Could you open up your browser’s dev tools and see if there are any specific network requests that are failing when the notebook gets stuck?
edit of Mar 6, 2019: not sure this is worth its own post, so I’ll add this info here. I’ve since noticed similar behavior in Chrome as described in your posts above (namely that attempting to load a notebook gets stuck with “Waiting for api.observablehq.com”) (it only happened very rarely when I was expermienting around this issue). I think the explanation is in @mootari’s post below, that a script is getting stuck in some other window and Chrome then refuses to proceed with Observable loading elsewhere. So far I’ve been able to fix it just by restarting Chrome though.