Why am I experiencing random bluetooth disconnects?

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 > General > Reset > 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