To reproduce:
1) Create new project
2) Mark it to Autoconnect to Profiler (it doesn't work when directly connecting)
3) Build and run for WebGL
4) Notice player connects to profiler and profiling data is gathered and shown to user
5) Close tab
6) Open new tab and go to same localhost that was generated for first time

Expected: Profiler works again once loaded
Actual: Player is shown as autoconnected but no data is outputed

Tested on Chrome and Firefox

Not reproduced in 5.5.3p1 (Connection is shaky and it can sometimes drop mid-session when losing/regaining focus, but it would always connect at start)
Reproduced in 5.6.0f3, 2017.1.0b1