This phone DOES NOT have a proximity sensor. Microsoft uses a simple software trick to turn the digitizer on and off. If you're in a call, and the top portion of the screen is being touched, it assumes you have the phone to your face and turns the display off.
I have owned an AT&T Lumia 635 since July. I have had the issue with the screen turning off while listening to visual voicemails before & after dev preview, and even on Windows 10 TP. To be fair, I am on Cyan, and maybe Denim will fix the issue. Maybe not. Otherwise, this is a shortcoming of NOT having a proximity sensor.
End-all-be-all solution: Buy a phone with a proximity sensor such as the 830. Even the 520 has a proximity sensor. Microsoft's decision to skip this important sensor, as well as the ambient light sensor (520 even has ambient light sensor), is one of the biggest shortcomings of this phone.
Supposedly, the 640 (& XL) will feature both a proximity sensor and ambient light sensor. Otherwise, you have no option on the 635 except to live with this issue during visual voicemail playback. I know it sucks, and will be replacing my 635 with a 640 the day the phone becomes available.