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In the layout, select you frame and right-click on it. Now select Frame Properties.
In the Frame Properties dialog, click on the Style button.
In the Region Style dialog change the Border Width option to Points and set the line width.
Finally, save the layout to a PDF again.
I tried creating a few inset maps and set the style to use a 2 point wide border line. That seems to work fine when I open it in Adobe Acrobat and zoom in and out. Even setting the zoom to values like 23%. The lines all look fine.
I made sure all the frames were using this line width.
I also tried creating the PDF in 600dpi as well as 150dpi. That didn't seem to matter much.
Have a look at the attached PDF and let me know if it also looks fine for you.