When a search is longer than 20 seconds, JIRA will not return the search result due to timeout set in the code. Even though it appear to be timeout in the UI,JIRA thread processing the request is still running.

So, a suggestion is to have the option to set the limit in the JQL search. For example, when running the JQL like "project=DEMO limit 15s" , the JQL should run only for 15 seconds and not more.