On the settings page, your settings are saved via non-personal browser cookies. The DuckDuckGo setting cookies are a reflection of your current settings as a URL (see below) but without the "k" parameter. For example, the region setting is notated with, "kl" and a Canadian region setting would look like kl=ca-en in the URL. The cookie for that setting, though, would be named, "l" and it's content would be ca-en.
If your settings keep getting cleared, that's because you have some process that is clearing your cookies (or you are switching computers). You could make an exception for duckduckgo.com from that clearing out process.
To avoid cookies altogether, you could use our URL parameters. To make the use of the parameters easier on the settings page there is a link entitled, Bookmarklets and settings data. Clicking this link will expand the Settings box and show you your settings as a web address (URL). You can set that web address as your homepage or as a bookmark/favorite, and then those settings should be respected thereafter (as long as you start from that page).
If you save that URL you can also use it to load/restore your settings from the bottom of the settings page as well. For example, you can email yourself that URL and then easily restore settings on different computers.
Finally, you can use the Cloud Save system to save your settings.
Prior versions on GitHub.