Reproduction steps:
1. Create a new project and import the Profiler Analyzer through the Package Manager
2. Open the Profiler along with Profiler Analyzer window
3. Make sure that Recording is toggled on in the Profiler and set to Play Mode
4. Enter Play Mode
5. Close and Open the Profiler through the Profiler Analyzer

Expected result: Profiler continues recording after closing and opening the Profiler through the Profiler Analyzer
Actual result: Profiler does not continue recording after closing and opening the Profiler through the Profiler Analyzer

Reproduces on: 2020.2.0a21, 2020.2.0b2
Does not reproduce on: 2018.4.28f1, 2019.4.12f1, 2020.1.8f1, 2020.2.0a20, 2020.2.0b6