Keep your Device Screen Awake for Select Apps with KeepScreen
Practically every mobile device has an automatic screen timeout feature built-in and enabled by default to save battery life. Android allows you to disable screen timeout when the device is charging, but you might also want to keep it from timing out when you have certain apps running—even when untethered from the charger. While several apps like media players and ebook readers do have wakelocks built-in, many usually don’t. That’s where KeepScreen can come handy. It does one thing by allowing you to specify the apps for which you don’t want the screen to time out.
The app was originally developed by AxDroid and released on the Play Store for free. However, it had several bugs that needed to be fixed, and was apparently abandoned by the developers. After trying to contact the developers to no avail, XDA Senior Member elesbb decided to fix it himself. He then ironed out the quirks and shared it with us. It even works when you have the Galaxy S3’s Smart Stay eye-tracking feature enabled, as long as the currently active app has been added to KeepScreen’s whitelist.
You can grab a copy of the app from the forum thread.