what level are your staff and are you travelling with either the scanner or the rank cheese to improve your odds?

Later in your game, when you've trained your staff to have lvl3 of skills (like Aerodynamics III for example), leveled them up (lvl20 is max) and achieved more stars across all your museums you unlock two really helpful items to craft in the workshop that help you get Pristine items more often but also the uncommon and rarely seen items more often - Rank Cheese and Survey Scanner. The Rank Cheese inflates total rank of you expedition team and the scanner +50% to location's survey level. You can use these items at any museum, not just the museum you unlock them in. When your staff are trained enough, they cancel out all negative events in an expedition and that's what you want, you want there to be zero negative encounters on the expedition so you can use the scanner or the rank cheese.

edit: sleepy typing

It's crazy frustrating but your odds do get better once the staff are just better and you have scanners and rank cheese to use.