I'm going to present this with little comment; you can read this thread at Fangraphs and see what spurred this (there is also some similar data there from "rotofan" and "Eric R").
I found the player who appeared in the most games as a DH for each AL team, 1973-2009, and then found the average games for the team leader and the percentage of teams whose leader DHed in 75, 100, or 125 games. Remember that games played include
This chart follows the average over time:
This chart shows the percentage of teams with a DH who played in 75, 100, and 125 games:
Personally, I think the average is the most interesting figure here, and it's hard to identify any sort of DH death throes from it. The percentage of teams with DHs appearing in 100 and 125 games has declined a bit in the last few seasons, but the percentage appearing in 75 has increased. Also, remember that with just fourteen data points each season, something like Travis Hafner getting injured can cause a big nose dive, despite the fact that Cleveland fully intended to use him as an everyday DH. Of course, the strike-shortened seasons of 1981, 1994, and 1995 also throw things off--the 1981 Brewers' leader in appearances at DH was in just 24 games in that capacity, the lowest ever.
The raw data