After the October MFM app/site migration, I had almost all the same problems as you (constant red icon, warning light notifications whenever I turned the car off.. I think I even got the incorrect clock warning once). About half the time, MFM could not connect to the car for status, remote commands, etc., but it would work sometimes, in "spurts". Glad to hear I was not alone... obviously, that collection of issues is not an isolated scenario.
For me, this all went on until New Years, when I finally had all the recall updates performed and MFT 3.6 installed. At first, the red icon didn't go away, but it eventually did (after a couple weeks). I'd say that MFM connectivity has improved back to where it was before the October migration (meaning, works 98% of the time). My only remaining issues are that the Trip & Charge log doesn't record the average Wh/mi like it used to (always zero or "--") and occasionally the log seems to be missing events (more often than I remember). Both of the latter behaviors started immediately after the recall updates were performed.
In any case, are you sure your car has all the latest software?
(Not that MFT likely has much to do with your issues, but do you have 3.6? I ask because I don't think that version has a daylight savings setting any longer, so I found it odd that you mentioned such a setting.)
