Though several Android apps have built-in wakelock mechanism to stay on, many don’t have. If you need a particular app to stay on, you can do it with a simple app called KeepScreen. KeepScreen helps you to prevent screen timeout when you’re using applications like browser, media player or like that. However, it’ll deactivate timeout only when you are using preselected apps.
How to use KeepScreen?
After installing KeepScreen run it and select the “Applications” menu. Click on the app that you want to disable the screen timeout. Run KeepScreen with the start/stop service menu, and then test by opening the application and see that you will never have screen timeout. Note: The app was originally developed by AxDroid and released on the Play Store for free. The bug fixed version can be download from this XDA forum thread.