Oh! I forgot about that one! We like that one as well. As to whether or not it jumped the shark, I don’t know. We still enjoy it. Does your wife still watch it? Or watch it to complain about it? 
As an aside, you really can’t talk about the ratings of an HBO series in the same way as you do about a broadcast series. The purpose of ratings for a normal series is to sell to advertisers. The purpose of an HBO series is to get people to sign up for HBO and/or stay with HBO. A series that get so much buzz that people not signed up for HBO feel they must sign up to see it first run is a winner, no matter what the absolute ratings are.
For instance, I’ll be getting HBO in April specifically for one reason: A Song of Fire and Ice. So I guess that’s a win in their column.
She still watches it, though there’s a lot of eye-rolling now.
That’s my point exactly… they’re aiming for the wrong demographic. I can’t think of anyone who watched Friends and/or Survivor religiously who would have watched Firefly no matter when it was on. I also know people who probably would have watched Firefly no matter when it was on… had they known it existed.
The actual demographic of Firefly WAS NOT the demographic they were targeting if they were thinking that the Friends/Survivor demographic was what they were looking for. This is the stupidity that I was talking about. By comparison, Star Trek: Enterprise lasted 5 seasons or more, and was a notably inferior show in most every respect, but it wasn’t abandoned on early Friday nights.
(and I’m a fairly big nerd, but also not an anime-watching, basement dwelling doofus either. I do know who watched Survivor, Friends and sci-fi shows like Star Trek:Enterprise, which was a contemporary)
Interesting article:
http://www.cnn.com/2011/SHOWBIZ/TV/03/28/fringe.ratings.go/index.html?hpt=Sbin
Apparently Fringe did well on Thursdays, then ratings fell significantly when Fox moved it to Fridays. Despite that, they renewed it, due to fan activism and interest.
Some kids’ action shows were aired on Fridays on the theory that it wasn’t a school night, before cable channel proliferation. These days, we call Friday nights (on commercial nets in the USA) the Friday Night Death Slot. The TV Tropes page (linked) has cases where a show started to succeed on Fridays & so was moved to Wednesday. Possibly on the theory that it didn’t suck after all & it could make money when more viewers would be home.