I haven't started playing with my Kindle Fire yet, but one of the main reasons I bought it was to be able to load songnbook PDFs into it, so as I learn to do that, I'll try to remember to check in and tell you what I know.

One quick first guess: these days, many PDFs are not made with Adobe Acrobat, but with other similar but not identical PDF makers. If you have the opportunity, you might try renaming and saving these PDF files using an Adobe product, as the Kindle app is an Adobe product. Not that I've tried it; it's just someplace to start.