I too am having the same problem. My web query is the same as what's shown in the original post in the VBA code box. When I let the code run without an "on error" statement it sometimes errs on the ".Refresh BackgroundQuery:=False" statement and when I choose debug and then resume it executes fine till a few queries down the road and it fails the same way. When I add an on error statement and have it do a resume with or without a 5 second wait it often fails the second and third times.
I had a similar macro working in 7 years ago under office 2000 using a dial up modem. Now that I have Office 2007 and DSL my upgraded version works very spottily. If anyone has a solution please post it.