There is no specific restriction for the session number. However, as your computer resources is limited, the number of the sessions is related to your hardware.
No, you are not right. I have many memory and disk space in my computer. With version 7.0 i can open seven session but with 7.0sr4 only five and report in notepad "Too many Origin sessions"???. This is not windows or computer resources limited. This is bug or spesial limitation of OriginLab. With very weak computer - 166MMX and only 48Mb memory I can open fourteen! sessions of origin 6.0sr4. :-)