CFPDF and Acrobat concatenated PDFs

I ran across an odd problem with a multipage PDF last week. I’ve been doing a lot of work with PDFs lately, so to make it easy on myself I created a few PDFs (generated with Acrobat Distiller) to work with in testing.
Each PDF was 1 page long, and I was using CFPDF to thumbnail each page of multipage PDFs, so I needed a PDF with several pages.
I used the Document->Insert->Pages From File function in Adobe Acrobat to create a 4 page document, and started running my tests. Over and over I only got the first page of the pdf, however.
Eventually, I recreated the PDF (unfortunately, I don’t remember how, but it was through Acrobat), and the thumbnails worked. I realize the subset of people working with Acrobat Standard and CFPDF is probably incredibly small, but hopefully I can save one person an hour of head scratching.