The main problem here is that a PDF is the electronic equivalent of a piece of paper. They are usually created in some other app, like Word or Pages, then converted to PDF for distribution. Applications that can actually edit (not just annotate) a PDF are rare, and usually limited in features. It won't be anything like editing a word-processing document.
That said, PDF Pen is probably the closest thing you'll get to what you want on the iPad. The computer version of this app can convert a PDF to a Word document (with some formatting loss). I scanned through the description for the iOS version and did not see this feature. But it does say it can edit a PDF.
I have not used PDF Pen myself; but have heard good things about it from some friends and acquaintances. There is both a basic and pro version, so read the descriptions carefully before deciding which, if either, to get. Visit their website as well, and ask any important questions there. Hopefully they have a good FAQ and feedback page.
Worst case, you should be able to copy&paste text from the PDF (using PDF Pen or another PDF app) to a new document, and create the resume again. This time in a format you'll have on hand, and be able to easily update.
Good luck.
P.S. Personally I use PDF Expert, which has fewer features than PDF Pen, but all the stuff I need, and I like how it works.