@CC_Stefan It’s not a browser feature, but (likely) a plug-in, or a configuration option of your web app.
I wouldn’t expect average users to even know how/where to selective delete cookies. Rather, these problems typically arise because:
a) there is a problem with the site’s plugin/option, where the cookie is not updated reliably under specific circumstances, or … (less likely)
b) the visitor has an overzealous browser “privacy” plug-in installed, that blocks writing/updating this particular cookie.