In general, puzzles are retained for at least two months unless you delete them, or for some reason I delete them as inappropriate. This allows you to email the puzzle URLs to other people, come back later to edit them, but also allows the web site to recover space from puzzles that nobody cares about.
If the puzzle is referred to after two weeks from creation, it is put onto a longer watch list. As long as that puzzle is referenced routinely, the puzzle will be maintained on this site (assuming that the disks and backups are working correctly). This means that you can put the URL for your puzzle into a web page, and expect that the puzzle it points to will live indefinitely.
I keep puzzles listed for the public for awhile. As long as there has been less than 250 puzzles in the category you listed the puzzle in, I keep the puzzle for others to enjoy. Sometimes I keep those puzzles in the permanent archive. But even the User Listed collection can be quite lengthy in time depending upon the category you list the puzzle in.
PDF files are not retained for very long. Don't put references to PDF files on web pages; the link will be broken in a short time.
Puzzles that come to my attention that are "inappropriate" (by my definition) may be deleted earlier than the above rules would suggest. I don't go out of my way to find "inappropriate" puzzles. I do look at puzzles listed for the public, but don't look at the vast majority of the puzzles.