Earlier quoted context omitted.
about the E-2 thing you said, it's only true if you applied within the US. if you applied and got an E-2 outside of US, you can freely leave and enter on it anytime.
I talked with an immigration lawyer last year. She told me that the period of free re-entry was only within 6 months of the visa issuance. I did check and found a list of varying periods for different countries on some website (I can't find it now.) However, I just found this paragraph on www.uscis.gov: "An E-2 nonimmigrant who travels abroad may generally be granted an automatic two-year period of readmission when r…
The durations may vary depending on the country the visa is issued from (due to the underlying treaty), and the status associated to it: in my case France as an essential employee (NOT as an investor).