Without a screen shot, this is shot in the dark, but it sounds like part of your AI file is set to overprint. If the part of the logo that is missing is "white" or "paper", then it will disappear in print and when viewed in Overprint Preview mode. This issue applies generally to any portion of a graphic, no matter what color, if the part of the graphic that is set to overprint is close to the same color as the background on which it's viewed. Hope this helps.
Similar to Mikey's response… If the logo has a spot color in it and it overlaps any raster image (or vice versa), then the overlapping part will appear white if "Overprint Preview" is turned off in Acrobat. This is really a bug. One possible fix is to export the PDF as an PDF/X-4:2010 in the "Standard" drop down—this preserves all transparency layering without flattening.
This issue causes frequent headaches and confusion in my workplace, especially since a lot of people want/need to hold on to the PDF/X-1a standard, which flattens the artwork.
I found a solution on this page:
Basically, it told me to make sure that the 'print as image' box was ticked in the print dialogue wondow. It worked for me as a complete logo was missing from my printout, even though it was there in the PDF on screen. Not very helpful when I have an advert booked in a magazine and they require a hard copy!
There's a wasted hour of my life!