The AccuWeather sync seems to work over the msyncd daemon running in the background (at least I found an awx sync plugin for this) and it looks like as soon this sync does not work automatically, the weather forecast disappears, it does not cache the forecast for this event view.

A reboot often fixed this for me. Also, you have to make sure you have allowed background connections, otherwise the msyncd is not allowed to do its sync.

The other possibility is to install MeeCast and replace the events view plugin of AccuWeather with the one from MeeCast (How-To is in the MeeCast thread). I've switched to this for a few days now and it works fine. Contrary to the AccuWeather plugin, the MeeCast indeed seems to do a caching of the forecast and still shows it (albeit maybe not the real state of a changed forecast) without any internet connection.