Using BIDS 2005, and I am having exactly the same problem, but in my case Flat Files (txt) are the source. Have left default at zero rows to skip. Only additional thing to add in my case is that my delimiter is ascii 0254 aka Thorn character, but the previewers for flat file sources and flat file tasks are showing data populating out the columns, and the data delimiting according to supplied ASCII value correctly....just not flowing to OLE DB destination.
"[Flat File Source ] Warning: The end of the data file was reached while reading header rows. Make sure the header row delimiter and the number of header rows to skip are correct."
Would really appreciate help.