I am not having any problems. I am currently on Modern using Chrome Version 42.0.2311.90 m. I also tried the Classic Connect and am having no troubles there.
Ya, it had been working even though apparently it was no longer supported - then stupid me had to go and mess with my Chrome Extensions and somehow it/I must've toggled something so GC recognized it as no longer being supported. :-/
Garmin has provided a solution/replacement for Garmin Communicator back before 2014. It's called Garmin Express. You need to install that and your activities will be sent automatically to Garmin Connect and if desired Strava and some other websites. It runs as a service on your computer and works independently from your web-browser. When I was using Garmin Express with my edge500 it worked flawlessly to get my activities to Garmin Connect. Between the time I connected my 500 to the usb cable and then opened my browser to Garmin Connect, then activities where already there.
Some people for some reasons have some issues with it working properly, but if you post the problem in the Garmin Express sub-forum, then actual Garmin rep's have been addressing those issues. There is a learning curve for some with Garmin Express as it does work differently and does more things.