The "Run now" feature you can use on a Sync is very useful if you don't want to wait the next execution date.
However, due to API Quota/Rate limit of requests per second and many other params, we have to limit the usage of this feature to our paid offers only and also for one sync at a time.
If you are seeing that selecting the "Run now" button is not starting your sync, be sure to wait that all your other syncs are done first. That could be sync already scheduled or sync you have yourself started.
Thank you for your understanding.