When the keyword search isn’t working, but the location one is, it’s because you have some code in your theme or any of the plugins altering the WordPress default site search (which the keyword search hooks into).
Quite often, disabling the plugin or a theme that is causing trouble is not enough. All (including bad and nonexistent) search results are cached as transients. After disabling plugins or a theme, you may need to edit any job posting (a slight change such as adding a blank is enough) and save it. Then try the keyword search again.
Relevanssi is one of the search plugins that enhances WordPress search functions. However, it doesn’t work with WP Job Manager, so the Relevanssi team created a short tutorial for disabling Relevanssi for WP Job Manager posts. You can check it out here.