My situation seems to have resolved, quasi-miraculously.
I was experiencing exactly what Paul Baptist described. wrt OS version, I had upgraded from Yosemite to Sierra mid-June 2017, a month ago. My Safari, 10.1.1, was last updated more than a month ago. My Remove DL List setting was Daily, which I can't remember ever having tweaked. I have certainly downloaded a few things in the last month, yet somehow I was noticing this disappearance just today. I noticed it first when viewing a PDF and clicking the download button. I experimented in different pages, downloading embedded images, etc. I changed my Remove DL List setting to Manual, quit Safari and restarted, etc etc. The toolbar item was not visible during downloads, and not visible in the Customize Toolbar sheet.
The resolution was: I went to my online banking site where I knew there was a page for downloading account histories using an actual "download" button. I clicked it, and it the toolbar item appeared. It now works for all the other types of downloads I experimented with, but with one exception: when viewing a PDF in a Safari window and using the download button — the one you have to hover your mouse to see — that action does not cause the toolbar item to appear.
