Hello BrooklynWM!
I'd definitely want my iPad staying connected to the Wi-Fi while I'm using it. Thanks for posting that other iOS and OS X devices have no issue with the connectivity dropping. We can try a few things.
First would be going through the steps listed in this article: If your iPhone, iPad, or iPod touch won’t connect to a Wi-Fi network - Apple Support
Then if that doesn't help out, you can check the network settings with this: Recommended settings for Wi-Fi routers and access points - Apple Support
After trying those, if you're seeing the connectivity drop still, make sure the iPad Pro is up to date with iOS 9.3.2 and check to see if the connection drops when you're in a certain location, time, or an event is happening elsewhere in the home.
Warm regards.