Phil - If you've cleaned the contacts with DeOxit, I doubt you'll do any better with isopropyl alcohol. So you're right I think - it's probably a lens issue.
If you love the 24-120 focal range and if it has served you well over the years, I strongly suggest that you owe it to yourself to try out the much newer Nikkor 24-120 f/4 VRII. It is a remarkable match for the D800 and it has been on my own D800 since last May. I purchased the newer 24-120 f/4 when it first came out three years ago and it has never let me down. The newer design is wonderfully sharp, contrast is wonderful, color is excellent and it's fast. A well built lens and one of Nikon's better efforts. The difference between both of the old Nikkor 24-120 designs (non-VR and original VR) and the the newer f/4 VRII version is literally like night and day.