I am also experiencing this issue. I've disconnected and reconnected both apps/websites from each other, deleted/reinstalled iPhone apps, and manually syncing via the website. No luck.
Garmin Connect seems to be pulling info in from my Vivofit and calorie info from MFP, but it is not sending calories burned information to MFP.
I had the same issue syncing yesterday, so I entered an activity manually into MFP. It later synced up on its own so I had duplicates in MFP and it Garmin Connect. I deleted the duplicates. All of that is a minor annoyance, no big deal, stuff happens, I didn't wait long enough or whatever, that's fine.
But now Garmin Connect keeps pulling in my manually entered MFP activity from yesterday over and over again, 5 copies so far (I have to keep deleting them). Hopefully it stops at some point!
(2 more just popped in again as I was typing this)
I'm having the same issue, activity from my Forerunner 220 is not being sent to MFP to update daily calories burned and I don't want to enter it manually for fear of what a previous poster said about duplicate entries etc. Not sure why Garmin seems to have ongoing issues with their apps and web interfaces they historically have good products. Maybe they need to hire some additional support for the software development team.
So after messing around with both of my profiles on Garmin Connect and MFP I found that if you switch to the date of the activity on Garmin's page in the Calories in/out section and click sync now which is printed in small blue text in the middle of the page on my computer it did in fact send the data from Garmin Connect to MFP. Not sure if this just happened to coincide with the companies fixing with whatever was broken but maybe you have to sync the individual date if it's past that date. Who knows, would be nice if it just worked from now on.
Actually, they say there is an issue and are working with Garmin to resolve it, but not that the problem is on Garmin's end. MFP failed syncing with Withings at the same time, so the problem looks like it's on MFP's end, in fact.