It appears to be a fairly common, generic type error message with a number of proposed solutions but not a universal one. I would try to export your timeline as a DV-AVI (File>Export>Movie) and burn this in a new project after adding DVD markers/menu.
The first LINK on "API failure" has some suggestions, plus links to other discussions. A Google advanced search on "API failure" and Adobe yielded many dozen articles.
As Paul_LS says, it's a common error, and can come from different operations. Do not limit your search to just PE, as Premiere (through PrPro 2.0 and PE) and Encore can experience these.
Paul_LS's suggestion is a good one, and is a common thread in many of these articles.
I came across this message today using CS3 on XP64. The problem seemed to be caused by my trying to save the .mov file to a different hard drive than the one the premiere project file was on. From what I see in the forums there can beany number of causes of this error message - my hard drive location issue was probably just one.