Try it with this search:
an entire block of smash car windows
I’ll have to test Searx, Grasp, & Kagi. Right now I start with DDG and bang out to Google (append !g to my DDG search) at least half the time.
So note to DDG devs: those Google bang searches had results that left me 
!
I am not a search engine engineer.
Here are some things it might be though:
It could be that the results you see first are cached on their servers, and expiring from that cache between your searches. however usually when something requested is pulled from a cache, the items lifespan in the cache is usually refreshed so it lives a bit longer.
It could be that certain they are NOT cached at all, and certain sites are rate limiting the DDG crawler hitting them and returning info to you, so DDG takes them out of the results as they cannot confirm the site is alive. I noticed reddit disappeared from the results and we all know about Reddit and their APIs here.
It could also be their ranking algorithm for results is not as deterministic as they want it to be, it could also be that way by design. Page ranking is a closely guarded trade secret, especially at big places like Google. DDG results will never match 1:1 with Google. Personally, I prefer DDGs results to Google.
Excellent analysis. Caching came to mind for me as well. Thank you for the interesting speculation!