The "Communication lost" is to be expected. With different clients, you can only keep one session open at a time to the QlikView server. "Open in server" makes the QV Desktop act like a QlikView plugin for IE-client. Opening an AP document in your browser at the same time will create a new session and will disconnect the other one. Moving to a different sheet or making a selection in QV Desktop will first restore the session and will disconnect the session in the browser. And so on...
Want to keep two sessions open at the same time? Use the same client on the same platform using the same account.
No client should ever crash anything. You may want to report frequent crashes to Qlik support.