Usually JWT tokens are generated on the server-side (by central authentication service, like IdentityServer) and used for accessing microservices API of the same application. In most cases JWT tokens have expiration time (minutes or hours) and when expired client should request new one from the auth service. If this is your case, you don't need to store JWT token for a long time - it's just a 'context' of your front-end part. When web page is fully reloaded, new JWT token should be requested, and this is normal behavior.
You can specify JWT auth header for all jQuery ajax calls in the following way:
var jwt = "your_jwt_token_value";
$.ajaxSetup({
headers: {
'Authorization': "Bearer " + jwt
}
});