This has come up before, check out this thread:
http://yabb.jriver.com/interact/index.php?topic=91336.0Win 8.1 tablets are special in regards to how display sleeping works, and there may not be a way for JRiver to effectively bypass this because:
When the display is turned off on connected standby capable systems, all running software (including applications and operating system software) become subject to a new set of activity restrictions. Windows Desktop Activity Moderator (DAM) suppresses legacy app execution in a manner similar to the Sleep state. It does this by suspending all applications in the user session and throttling all 3rd party services to create predictable power usage over the period of idle time. [emphasis added]
My understanding is that means that applications other than "Modern" apps (i.e. win 8.1 appstore apps) are treated as though the system is suspended in connected standby.
The short term solution: if you need playback to continue try checking the JRiver option to "disable display from turning off during playback." Other users had good success with that setting. It will negate some of the power savings (because the screen will stay on during playback), but will allow JRiver to continue playing and you don't have to turn off connected standby off.