When I try upload some file to my extension the popup lose focus and close, can I make it persistent and maintain always open?
You can’t unless for development purposes, but in released addon it’s broken:
You have to reopen popup.html in the tab. I know, pretty bad UX 
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But when I reopen the popup it’s start at main menu, there is a way to reopen menu where I select a file?
I’m not sure I understand the question.
But in general, you need to tell user that he can’t select a file through the popup and add a button “Reopen in a new tab” which will call something like browser.tabs.create({url: "/popup.html"}), which will open new tab where user can load the file.