I'm not sure if this is a MyLink issue or a (android) GrooveShark app issue?
When I had my 2012 Camaro, I didn't have this issue at all using the same GrooveShark app. It would play without issue.
A couple of weeks ago, I traded in my 2012 and bought a 2014 1LT.
When playing bluetooth audio using GrooveShark app on my phone (similar to Pandora or IHeartRadio), it's like bluetooth and my phone gets out of sync and MyLink will say "Paused" yet the GrooveShark app says it's still playing and still shows as if it's connected to bluetooth. If I hit the play button on MyLink, nothing happens. But if I hit pause *ON THE PHONE* to pause the music, then press play it will resume playing through the radio again.
It has completely ruined my MyLink experience considering it worked so smoothly on my 2012 1LS which I installed a PDIM module on, yet my 2014 1LT nicer model can't handle doing the same thing...