That would be 47 seasons in the NFL. Yep, only 13 times in 47 seasons is pathetic. And like you said, 10 came in a 12 year period.
As an AFL team, they made the playoffs 4 times (all in a row) in 10 seasons. So, that's 17 playoff appearances in 57 seasons.
How about this: the Bills have been successful and made the playoffs with only 4 head coaches. Lou Saban, Chuck Knox, Marv Levy and Wade Phillips.