Growing old with your audience is a great long-term strategy. I give you KOST as an example.
Refusing to grow old with your audience can leave you left behind in a cloud of dust sooner than you think. I give you Rick Dees as an example.
In addition to David's point about KOST, Rick Dees had a 23-year run in mornings on KIIS by (largely) keeping up with the times. The number of morning shows in Los Angeles that have had that kind of longevity at the same station is a small one. Dick Whittinghill (KMPC) and Kevin and Bean (KROQ) had 30, Mark and Brian (KLOS) managed 25, Mark and Kim (KOST) 21, Ryan Seacrest (Dees' replacement at KIIS) 16 and counting.
And in L.A. CHR/Top 40, Dees is far and away the longevity champ. Robert W. Morgan had five years and five months at KHJ the first time around, 14 months the second. Charlie Tuna had two 14 month stints there five years apart. Charlie Van Dyke did three years and nine months.