Postgres users occasionally encounter "remaining connection slots are reserved" errors due to exceeding the maximum number of simultaneous database connections defined by the max_connections setting. This error occurs when a high number of simultaneous connection requests from the same Postgres user surpasses the limit for their database. Neon, a managed Postgres service, sets max_connections based on the size of your compute instance and its memory. To avoid these errors, users can find and remove long-running or idle connections, upgrade to larger computes with higher max_connections settings, or enable connection pooling using PgBouncer for up to 10,000 simultaneous connections.