The “Auto-close delay” (in days) can be set in WP-Admin > Awedesk > Configuration > Advanced > Cron, as explained here: https://awedesk.com/documentation/config/cron/

To keep the ticket open and avoid auto-closing, you should enable “Prevent auto close” as shown below:

All such changes (enabling and disabling) are recorded and shown in the ticket (agents and clients see them) as below.
1. Prevent auto close was enabled
2. Prevent auto close was disabled (the auto-close delay feature was triggered in that case)