Your software doesn't work with iOS 10 on iPhone or iPad. When will this be corrected? Look at the "one star" ratings in the App Store and read their comments. Look at the Sling Community notes.
I have exactly the same problem and the common factor is SlingPlayer and iOS 10.
I have been using SlingPlayer on iPad and iPhone for years with no problems until upgrading to iOS 10 and the latest version of SlingPlayer.
Here is my current status (each connecting to Slingbox Pro-HD):
iPad iOS 10, SlingPlayer 3.4.9 = complete failure / totally unusable
iPhone iOS 10, SlingPlayer 3.8.51 = complete failure / totally unusable
iPad iOS 9, SlingPlayer 3.4.7 = WORKS PERFECTLY
When will Sling correct the problems that they have with iOS 10?
Can we get a copy of 3.4.7 for the iPad in the meantime (or will that not work with iOS 10)?
Is it working via web browser on a computer? If it isn't due to iOS 10, it could be your PRO-HD failing due to power supply or capacitors on the board.
Mine kept locking up/freezing and I changed the 3 capacitors on the board and the power supply and it works great ever since (did the repair several years ago).
1) Ordered a new power supply from Jameco.com, Jameco Part no. 379623 (i purchased from jameco because the power supply is more reliable than the one from sling)
2) Soldered 3 new capacitors (470Uf, 35volt) on the board. There's a lot of videos on the web for how to do this. Just google replace sling box capacitors (they often fail) In the end, the combination of the two has resulted in my sling box performing rock solid and it only costs $20 for the power supply and capacitors. I had to buy a solder gun but it's a worthwhile investment to have and not a bad skill to have (it's pretty easy to solder).