Hi, @TaniaFuchs. There is no possible configuration to get notified on the creation of a new sync error. You'll only be notified automatically if the connector is suspended.
Ideas asking for this have cropped up on the ideas board, like this recent one on creating a report from sync errors. Similar ideas have appeared previously, and I recommend searching and upvoting the most relevant to you.
Brad Mampe, Salesforce Analyst, Fidelity I'm probably wrong. I may not be right about that.