Whenever I had problems with admin Index Management, I just have to go to the CLI/Command and execute the command line to reindex specific or all indexes to fix the issue. This was suggested by the community and wondering why it works on the command line and not in the Magento Admin Index Management.
I guess it essentially comes from the : difference between PHP and PHP-CLI
For example, the
php.ini may differ and you will have different timeout or memory settings.
It depends on memory limits and execution time of php defined on your server. CLI doesn't have this restriction.