Some of you folks on this board are blatantly ageist.
It did cause me to look at the records of some of those "over the hill" coaches. to see how their records late in their career compared to their record over the entirety of their career. If indeed they are coaching beyond when they should be, their record should drop off. Now, some of the coaches mentioned had to vacate some wins, but that's a different problem that has nothing to do with whether they were too old to still coach, so I included the vacated wins in my analysis.
Paterno:
Last 5 years: 46-15 .754
Earlier years: 363-121-3 .748
Bowden:
Last 5 years: 38-17 .691
Earlier years: 339-112-4 .749
Beemer:
Last 5 years: 41-21 .661
Earlier years: 225-111-4 .668
Solich:
Last 5 years: 38-23 .623
Prior years, Ohio only: 32-31 .508
Prior years including Nebraska: 90-50 .643
For Beemer and Paterno, there is not much difference between their records in the last 5 years from their records in earlier years. When you consider that their final five year were probably harder than their earlier years (with Penn State having moved to the Big Ten in 1993 rather than playing an easier independent schedule, and with Virginia Tech having moved in 2004 to the ACC), their records over their final 5 years is probably more impressive than their longer term career.
For Bowden there does appear to be some dropoff in his final 5 years.
For Solich, hit most recent 5 years is significantly better than his earlier years at Ohio, and nearly equal to his earlier years even including his years at Ohio.