Plenty of patterns can survive in some degree of static. One of the rules is "Any live cell with two or three live neighbours lives on to the next generation."

Plenty of patterns can survive in some degree of static. One of the rules is "Any live cell with two or three live neighbours lives on to the next generation." Therefore, a spaceship cell that normally had two neighbors could run into an extra blip, and there would be no effect. As far as specific patterns that are just generally resilient, Life patterns tend to be pretty fragile, and I would expect this to be an unavoidable consequence of the game's rules, one that would scale to any complex construction you built. Also, I'm not going to attempt a proof but it sure seems that for any pattern X, you could construct a (pretty simple) pattern Y than would destroy it.