Yes. Messaging your Matches is included in Free Access. Neither of you needs Premium to message each other, provided your accounts remain eligible and messaging is available.
Premium gives you access to First Likes; it isn’t required to continue an eligible conversation. When Premium ends, that alone doesn’t remove your Matches, delete your conversations, or stop free messaging.
A conversation may become unavailable if either person blocks or unmatches the other, deletes their account, or loses access. Safety and technical restrictions may also affect messaging.
A Match doesn’t guarantee a reply. Respect the other person’s boundaries and stop contacting them if they ask you to.