Why am I experiencing random bluetooth disconnects? I have an iPad Air 2 64GB now running iOS 8.3. I've experienced problems where when using Keynote on my iPhone 5S to remote control a keynote presentation on my iPad, the connection will be dropped at random times during the presentation. I attributed this to Keynote bugs, but then my iPad also started randomly losing connections to my Logitech Ultrathin keyboard cover (the onscreen keyboard would appear) or I'd type a certain character and it would start repeating ad infinitum. I removed the interference factor from the equation by noticing that the problem would also occur within my office with thick walls and no bluetooth devices nearby … so I had Logitech replace the keyboard, but the connection drops still occur. I also reset all settings on my iPad, which didn't help.

So my next question is this: could the bluetooth hardware on my iPad Air 2 be flakey? Everything else about it works fine.
It sounds like you are not alone and no fix in sight at the moment according to this report.
How to potentially fix iPad Bluetooth Problems

iOS 8 Bluetooth problems are among the most common iOS issues and they
were a big problem inside iOS 8. We ourselves have run into iOS 8
Bluetooth issues with the iPhone 6 and iPhone 6 Plus and while iOS 8.1
delivers fixes for Bluetooth issues, we expect Bluetooth problems to
persist inside Apple’s brand new iOS 8 update.
There doesn’t appear to be a cure all, we’ve heard about a few
possible fixes that iPad users will want to try. iOS users have
singled out “Reset All Settings” as a solid fix. It hasn’t worked for
everyone but there are a ton of people that are claiming success after
trying it on their iPhone. It should work for Apple’s iPad as well.
To do this, open up the iPad and head to Settings &gt; General &gt; Reset &gt;
Reset All Settings. This is going to take a bit of time and users will
lose all saved settings but the pay off is that it seems to be fixing
Bluetooth issues for many people. It’s certainly worth a try if
Bluetooth keeps acting up after Apple’s iOS 8.1 upgrade.

For the time been, you can file your report with Apple and hope for the best.
https://www.apple.com/feedback/ipad.html