I recently purchased and installed Sitemap Generator and am having a number of problems:

1.  Many URL's are missing from the Sitemap ( roughly 100 out of 1000).
2.  Sometimes sequential Crawls will cause some files to be dropped; others added, when the web site hasn't changed. Sometimes, when you crawl again, then what was previously dropped is added and what was previously added is dropped.
3.  When I remove "pdf" from the list of "do not parse extensions" I can see that the pdf files get parsed by observing the crawler's progress messages. However, at the end, none of the pdf files are now in the sitemap. When I change the configuration again and put "pdf" back into the list of "do not parse extensions" and recrawl, the pdf files again appear in the sitemap.

could you please PM me your generator URL and an example URL that is not included in sitemap and how it can be reached from homepage?

You should have "pdf" in "Do not parse" setting (which is default), in this case they would be included in sitemap.