For better or worse, Preds' owners have come out and said they're not hockey savvy enough to make hockey decisions. I think that based on past contribution and reputation for making chicken salad out of chicken ****, trotz and Poile can basically stay as long as they would like. That was the mindset in Buffalo for a very long time, and it took a new owner to change it.
I don't think coaching is the entire problem, though there are some hallmarks of Trotz teams that have followed him through his career. Poile worries me a little more, given that he's got a pretty miserable track record that spans 30 years at this point.
I don't know what it would take to actually incite a change, and you can say "the Predators make the playoffs every year," but they also haven't gone beyond the second round. I gather it would take 4 or 5 straight years of bad teams for someone to lose patience, and with Pekka and Weber, that's not likely to happen so...sadly, we have what we have: a team that will always be pretty competitive and win games, but will never get over that last hump to be a true contender. It's the David Poile thumbprint.