Are they possibly comments or markups?
If so, be sure and have comments and markups selected in the print menu.
I tried changing Markups/Stamps, but that didn't help. What I did find, however, is that if you go into Advanced in the print window and check the box "Print as image", then all the lines and borders will print just fine. I don't know if this is the ultimate correct answer, but it worked for me. The forms I was trying to print were the tax forms such as the Form 1040, etc., at the irs website (irs.gov). This has also happened to me when printing PDF maps where certain symbols and icons on the map do not print out for some reason. Thanks for your help!!