WordPress gets constantly updated and every update brings new features and fixes bugs.

Will the plugin no longer work with a WordPress version which is no longer supported?

No, if the plugin worked in the past it will most likely work in the future.¬†Sometimes features not available in this version will cause an error which no longer get fixed.¬†Also there’s no dedicate test for deprecated version.

In general I recommend to keep your WordPress site and it’s plugins up to date to prevent security vulnerability.

Read more about updating WordPress.