I've seen this asked a few times on Meta.SE and I believe this answer is still current:
How was this answer posted after this question was closed?
The message that you see not allowing an answer to be posted happens on the client side of things, the server allows a grace period of around four hours. So one likely cause is that Jim had it open in his browser for some time and that check failed. Or maybe he did the same using the mobile version of the site that according to that answer doesn't have that check.
The real-time updates you see on questions (votes can change without refreshing etc) use a WebSocket on modern browsers but some operations fall back to XHR on older browsers. Looking at the JavaScript involved I had a bit of a problem understanding some aspects, but from what I could work out the ability to post seems to get disabled in the client browser as a result of a message back from the server so if that fails (WebSocket is closed / times out while the page is still open) you can still post an answer.