The problem is after an restart or config change the Nagios core inside CRE needs some time to be available again for livestatus queries.
The time needed depends on different things. One thing is the overall load on the system that looks ok, On other thing is how big is your status file or how big is the log file from the current day. These two are reloaded an processed/cached inside the core.
To troubleshoot or to know where the problem lies you can do not so many things.
If you have enough resources on your machine make a clone of your site.
Stop booth sites, inside the clone remove all Nagios core log files and also the retention.dat. Start your site and take a look how long it takes before the livestatus is available to queries. Then do a config change inside the cloned site apply the changes and measure the time again how long it takes. Compare the results to your productive site. There should be a difference without the log files.