Error 'LIMIT EXCEEDED 'Email-to-Case: Errors encountered while processing' received via Email-to-Case

This error is generic and can be caused by several org-level configuration or feature limit issues. One common cause is related to Omni-Channel routing configuration. Omni-Channel for Administrators.
Omni-Channel is a Salesforce routing feature that automatically distributes incoming work items — including Cases, phone calls, and chat sessions — to available agents based on their capacity, skills, and availability. Omni-Channel has defined queue and routing limits.
If Omni-Channel is enabled in the org and Email-to-Case is configured to route cases directly to an Omni-Channel queue, the following scenarios can cause case creation to fail:

• Specific Omni-Channel queue limits prevent triggers, workflows, or assignment rules from adding items to the queue.
• The maximum number of queued but unrouted records (default limit: 1,000) is exceeded, causing case creation to fail at inbound processing.

Resolution Steps

1. Verify whether Omni-Channel is enabled in the org and whether Email-to-Case is routing cases directly to an Omni-Channel queue.
2. Configure Email-to-Case to route new cases to a holding queue instead of directly to the Omni-Channel queue. This prevents queue limit violations at the time of case creation.
3. Use Scheduled Apex or Time-Based Workflow Rules to assign cases from the holding queue to the Omni-Channel queue shortly after creation, giving the system time to process routing rules.
4. Review Omni-Channel queue capacity limits in Setup to ensure they are appropriately configured for your inbound email volume.

Note: There may be other causes for this error unrelated to Omni-Channel. The above guidance addresses the most common scenario. If the issue persists after reviewing Omni-Channel configuration, escalate for further investigation.