Yes, there is no need to update the CSRF token. It just needs to be unique per user session.
As there is no way for an attacker to read the value of the hidden form field, the same value can be reused during the session. No extra security is accomplished by renewing this value.
However, it should definitely be a unique value per user session. Different users should have different tokens, and if the same user logs in again it would be a good idea to expire the previous token.