The offending line of code is 'Sheets(tab_name).Cells(74, 2).Value = Sheets(sNewSheet).Cells(i + 206, 1).Value.'
While I've never run into the paste limit, I could see how it happens. What you're going to have to do is manually call the clipboard C API functions and do the copy and paste yourself. Charles Petzold's seminal "Programming Windows" shows how to do it in C. Additionally, there are plenty of code samples around the Internet on how to use the clipboard directly from VB.
This was first published in August 2002