Well, before searching for an app to do this. As a human how can you tell if the date/time is correct without internet?
A possible solution would be a service which counts seconds from the last time the device was connected to the internet (which means it had a correct date/time at that moment) then when you want to add the new amount you can add the seconds to the last time and store this value.
Edit
You will 2 things to achieve this:
One more thing You need to be careful if the device goes off or for some reason, something stopped the service. All of these are user issues and you need to decide how much you want to handle stuff for the user.
You can fix user mistakes by pushing to a SqlLite
database every 10~15, but this won't fix if the device went off for hours and then started again at a wrong time - I don't think there is a possible solution for this-.