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You could try disconnecting it from Strava and reconnecting? Then record a brief activity and try uploading again. I've only had issues like you describe once and I think it was a Suunto issue with their service in the end. It's normally very reliable.
You can download the activity from Suunto and upload to Strava manually so you don't lose a run but obviously not something you want to be doing for every run!
Have you linked your Suunto account to Strava and did you do this before you uploaded the activity from the watch?