No. As long as you are getting the time using DateTime.Now then your app will not affect the clock precision.
It is possible that your app is leaking a resource and after a month it runs very slow.
Does the clock show the correct time after you restart the app?
Overall, mobile devices are not really built to run apps forever. It is a good practice to kill the app after 24 hours and restart it. You can do it with a second "watchdog" app.