I think that these two quotes from Tim Cook during the last Apple quarterly call, put the nail in the coffin:
"We've got the largest app store ..."
"... iPhone's integrated approach is materially better than Android's fragmented approach, where you have multiple OSs on multiple devices with different screen resolutions and multiple app stores with different ... "
Since Apple itself uses the word generically, I don't see how anyone can argue that it's not.
Isn't this what Amazon filed recently?
There are some interesting reads about trademarks on Wikipedia. I think one of the reasons Google doesn't want people to use the term "google it", is because it makes the trademark generic, and they can lose it.