As mentioned in Zabbix Documentation 3.0,

unsupported items are considered to be rechecked by [Refresh unsupported items (in sec)], but Zabbix do not activate unsupported item every N seconds set here.

Steps to reproduce:

1. Configure an external check item like attached (Update interval (300s), Refresh unsupported items (600s))
   Item key test2.sh like below.

   #! /bin/bash
   
   #sleep 60
   echo 1
   

2. Make sure you can get value, then delete the "#" in front of [sleep 60] in the test2.sh script, make it timeout and become [not supported] status.Please refer to below log.

   7794:20190704:185923.437 item "test_external:test2.sh" became not supported: Timeout while executing a shell script.

3. Add "#" in front of [sleep 60], make it works normally, then you can checkout this item activate after 300s, not 600s.Please refer to attached Screen Shot 2019-07-04 at 19.06.28.png and log below.

   7793:20190704:190420.665 item "test_external:test2.sh" became supported

It can reproduce most of the time, but sometimes it makes sense activate the unsupported item by [Refresh unsupported items] (600s).You can try several times above steps to checkout different behaviors from Zabbix Documentations.

Best regards.
Syusei