Thank you all for helpful comments/suggestions.

As there were hints related to 'order', I found that none of the sys_script_clients is given any order. Can that cause this issue ? Is it a standard practice to specify the 'order' to avoid such anomalies ?

I am inclined that this may be a problem with 'order' because my minimum expectation is 'onLoad sys_script_client' should at least be seen in console log of Developer Tools. "sys_script_client not working as expected because of any error" is a second part but at first I believe it should be executed onLoad of the page.

Also, there were few suggestions to add alert/log but unfortunately this issue is seen only in production so I am restricted from adding alert/log. Existing logs are also limited prohibiting root cause analysis.