Sakhmet Solitarie and Pyramids are indeed randomly possible/impossible to win. I mean, even if you make the correct decisions based on optimal gaming, you will not win a big percentage of times. If you are not fully sure about that, I suggest you to pick a deck of cards of your own and reproduce the game you're playing. Even if you play badly, in some games you will not be able to win. Once I was able to take only one card off the pyramid.
From my experience playing the solitaire games, I found that some solitaire games I cannot win just due to math and card placement. Usually, this situation t happens if you do not play a good version of the solitaire game. After starting playing the (you need an account to see links)on the Freecell platform, I felt the difference. Yes, sometimes it is very hard to find a good solution to shuffle the cards, but you can always find a proper exit, even if it takes a long time to think about your next move.
I can confirm the game's RNG is stacked against you winning, especially twice in a row for the gold bonus trophy. I initially tried to get this legitimately because I got really lucky on the similar trophy on Pyramids, but I got so tired of losing on Solitaire that I ran an autoscript for it. When I finally got the trophy, it had played over 2000 games, no joke.