Garmin has broken the API that RunGap and many other apps are using to connect to your data on Garmin Connect. This may take a while to fix permanently - so please be patient.
At the time a writing a temporary fix has been made and the connection works normally.
In case the connection breaks down again you can use this workaround to import new workouts from Garmin Connect to RunGap.
1) Log into Garmin Connect with Safari on your iPhone or iPad (http://connect.garmin.com).
2) Open the activity and tap "Export" and then chose "TCX File".
3) When the file is open, tap "Open in..." and next choose "Open in RunGap".