First part of that time period, they lacked an impact center. Stastny was an okay bandaid, but he was injured all the time and never meshed with anybody. They finally got Schenn last year, O'Reilly this year, and Thomas coming along, so the center issue is gone; but their goaltending, overall speed, and defensive depth has not improved (mostly due to Bouwmeester and Gunnarsson fading). Factor in some untimely injuries and some questionable coaching and here we are.
Their core is still fairly young (younger than most people realize, it seems) and they have some great talent coming along. They just need that talent to arrive with a bang fairly quickly or they need to retool and bolster that next wave of talent.
They've done a solid job of building around Pietrangelo, but he was their only high impact addition by drafting high. The teams that have climbed past them lately are built around several high-end players acquired by drafting high repeatedly. As good as those later draft picks have been for the Blues, they aren't quite up to the same impact level. They needed to be worse for a little longer several years ago or they need at least one of those later-round steals to become elite. Parayko is good but not there. Fabbri's injuries really carved away that chance. Dunn is a work in progress. Husso is still unknown. Thomas, Kyrou, and a couple other guys have serious skill, but need more time. It's a rough place to be as a GM. The rebuild roadmap wasn't quite as clear as it is now, but maybe Armstrong should have seen it coming and tanked harder a long time ago, dunno.