Accented characters missing in selected font in PDF form

I have a PDF form, where I selected a specific font that must be used (i.e. Avenir LT Com). The font is legally installed on the machine and the PDF form is used only on that machine.

The font works in a form, except all accented characters are not in Avenir, but Arial, like the font doesn't have them - but it has.

I have used this workflow before and it worked for different non-standard font no problem, but for this and several others it doesn't work. Why it works for some, and why not for others? And why why why it works half-way, without accented characters?

I have Acrobat DC (CC subscriber) and Windows 7. Tried another machine with the same problem.

Thank you very much