Logging in earlier to my account was a little scary ... the website refused to load properly, even after many 'refreshes'.
Finally it loaded OK, and then offered the firmware update.
For me, updated and all OK ... but I DO REALLY NOT FIND this Trezor service to be always available.
... I don't like 'Intermittent' service long term.
If you really want to, you can run your own MyTrezor website and use that if the main one is down.
Here's a link to the Github page for the MyTrezor site:
https://github.com/trezor/webwalletAlso, firmware update went well for me. I haven't tried anything out with it really, but I'll have to look into the changes. I know multi-sig support was added, but only with Greenaddress right now. Hopefully soon we'll see it on MyTrezor as well.