Prakash, are you running the software in the Mendix cloud or are you using an on-prem deployment? If you are in the Mendix cloud, I recommend checking the environment tab to ensure you are updating the value for production and not for Test or a lower environment. That is a mistake we have made before. If you are indeed updating the correct environment, then it sounds like something support would need to take a look at. Those values should be updating when you set a new value.
Have you restarted the environment after changing the constant?
When you change the constant, the “New” value should update, and on re-deployment the “Current Value” should update to the new value
If you did only update your constant in the modeler, you only updated the default value of it. If it was already deployed before, you also need to change the value of the constant on the server. (In the cloud portal environment settings or in the yaml file of your on prem instance).
If you're not running in the mendix cloud, but for example on a linux machine, your yaml file is probably not valid.
If it's not valid, the application will always use the default values.