If the Email Hub stops pulling new messages, walk through these three checks.
Check 1: token expiry
OAuth tokens can be revoked by the user, by Workspace admin policy changes, or by Google/Microsoft when account passwords change. Open the Email Hub account settings — if you see "Reconnect required", click it and re-complete OAuth. The connector will resume from where it stopped.
Check 2: label or folder scope
If you originally synced only the "OMB-Sync" Gmail label, new emails that don't carry that label won't appear. Either update the Gmail filter rule, or expand the label scope in OMB Cloud account settings.
Check 3: throttling
For very large inboxes, Google/Microsoft enforce per-account API rate limits. If you're seeing slow sync rather than complete stoppage, the connector is being throttled. It will catch up over a few hours; no action required.
Force a manual resync
From account settings, click "Resync" — this re-reads the last 7 days of messages without duplicating already-ingested ones. Useful if you suspect anything was missed.
Last resort
If none of the above works, disconnect and reconnect the account. This is non-destructive: ingested history is preserved.