My deep apologies for this - I know this must of been exceptionally difficult for you. The outage was relatively short (~20 minutes) and we were taking steps to fix it within a minute of it occuring.
Construct 3 if already loaded should work absolutely fine even if the site goes offline and you're logged in. There may be issues using access codes or logging in if the site is offline.
To address this, we're going to be moving the login system to it's own server away from the main website to significantly improve robustness and ensure that Construct 3 will continue to work.
As I've said in email, it really does pain me to hear this feedback but please be assured I am giving this my full attention and am taking steps to prevent it happening again.
For what it's worth, downtime is now currently quite rare. We do update the website regularly (sometimes a few times in one day) which would cause a few minutes each time - I'm going to change this practise to only one update a day where possible during a quiet period Mon-Thurs to reduce impact here also. Once we've moved the login server to it's own server, website updates wont impact Construct 3 access any more either.