Steps to reproduce:

1. Download the attached project (replaykit-api-test.zip)
2. Switch to iOS and build
3. Build and deploy Xcode project to iOS 13 device
4. When launched, click 'Check APIAvailable' button
5. Notice the text that shows ReplayKit.APIAvailable value will change to 'false'
6. If you click 'Check APIAvailable' more than once, the subsequent times it will correctly return 'true'

Reproduced with: 2018.4.19f1, 2019.3.4f1, 2020.2.0a4

Tested with:
iPhone X (iOS 13.3) (Reproduced)
iPhone 11 Pro Max (iOS 13.3) (Reproduced)
iPad Pro (iOS 12) (Not reproduced)
iPhone 6 (iOS 12.2) (Not Reproduced)