While they have been okay, and Hayes makes up for one first round pick, I believe the Rangers are going to go 4 straight years without a first round pick. That catches up to you over time. Look at Pitt for an example.
The Rangers problem isn't that they're getting old. If anything, they are in for a cap problem. They have several defensemen signed for $5 million a year for several years, $8 million on a goaltender that is probably going to decline a bit starting in 2 or 3 years, and a lot of RFAs to lock up, many of whom are due for big raises.
Actually, the cap may be what has (or will) cost the Rangers this season. They lost their forward depth from last years team. Their major weak point comparatively this year is their 4th line. That doesn't hurt you in the regular season, but it does in the playoffs.