How would you troubleshoot a prospect who is not syncing to Salesforce?

I work through it in order, cheapest checks first.

First, is the prospect eligible to sync at all? The most common answer is that they are unassigned — assignment is the usual trigger for a prospect to sync. Second, is the prospect marked as deleted or sitting in the Recycle Bin, or flagged as a deleted CRM record? Third, are there sync errors on the connector? Field-level errors, most often a picklist value in Account Engagement that Salesforce does not accept, or a text value exceeding the Salesforce field length, will block the record.

Then I check the Salesforce side: validation rules, required fields, or an Apex trigger on Lead can reject the incoming record. Duplicate rules set to block rather than alert are a frequent culprit. Finally I check the connector user's permissions — if it lacks field-level access or object permissions, writes fail.

Prospect Audits is useful throughout, because it shows exactly what changed and when, which usually narrows down where the process stopped.