The latest issue seems to be that it just takes a couple of minutes to load in. The starting with clear bit was for repeat flights. The issue was (several updates back) that you'd finish one fight on live weather, then set up another one, but all you'd get is clear skies. For that, Asobo said to start your first flight in clear weather, then select live once you've clicked Fly Now.
Personally, I haven't seen this issue. It may be related to which regional server you're on.