I am using the Django rest framework JSON Web token API that is found here on github (https://github.com/GetBlimp/django-rest-framework-jwt/tree/master/).
I can succ
Yes, it's correct to say that JWT tokens are not stored in the database. What you want, though, is to invalidate a token based on user activity, which doesn't seem to be possible ATM.
So, you can do what you suggested in your question, or redirect the user to some token refreshing endpoint, or even manually create a new token.