The easiest way to lose trust in an acrobatic partnership is to make a mistake that hurts the other person.
This is usually a case where the base "drops" the flyer. Even though this is often not the base's fault, it doesn't matter - the base's job is to protect the flyer no matter what. Even if the flyer flails, or turns incorrectly. Even if someone from another stunt-group falls into your trick. Even if the base's wrist sprains and he can't hold the trick up.
The base still has to do everything they can to save the flyer. That will preserve trust best.
The flyer can lose trust by flailing, not staying tight, or panicking. This usually hurts the base, and it can easily hurt the flyer as well by taking away the base's responsibility to keep the flyer safe.
Another way to damage trust is through arrogance. I tell my flyers not to work with bases if they ask for a spotter and their base refuses based on arrogance, such as, "I've got it." An arrogant or showboating base will, sooner or later, injure a flyer and possibly himself.