Would you describe your problem in more detail? What is the mail app you use on your iPad Air? Apple Mail (the default mail app for iOS)?
"the iPad Air doesn't open with PDF"
When does it fail to open on your iPad Air? Do you see the PDF attachment icon in an email message in your mail app? What happens when you try to long press (press & hold) on the icon? Can you actually select "Open in Adobe Reader"?
Unless Adobe Reader is the one showing an error message (e.g. "invalid PDF") when you try to open a PDF attachment, it sounds like Adobe Reader (app) is not directly involved.
Could you also try to open an email with a PDF attachment in other iOS apps like Outlook Web Access (OWA), Gmail, Yahoo Mail, etc.?