Answer
Links normally expire after about 24 hours and also stop working if the inviter has left the chat. Old invitation links also stop working when a formerly shared chat becomes private; its remaining owner must issue a new invitation to share it again. If signed out, sign in and continue with the valid invitation; Hashchats remembers it and joins after you sign in. If that join fails, you are told once. A full chat stays saved and is retried quietly later. A deleted chat or a chat at its participant limit cannot accept a normal join. Joining gives access to the existing conversation history.
On updated builds, if you already belong to the chat, a retained old invitation can open that existing chat quietly even after expiry. This does not let a nonmember join or rejoin through an expired or invalid invitation.