😞
I believe the cookie you're looking to preserve between tabs is "esri_aopc" - I would suggest ensuring your Enterprise is fully updated, with all available patches, and then testing on a Browser that doesn't have any policy applied to it.
If you can still replicate the issue in this state, please raise this with technical support - it sounds like it will require a thorough investigation.
Hope you get to the bottom of it!
"We've boosted the Anti-Mass Spectrometer to 105 percent. Bit of a gamble, but we need the extra resolution."