If Sky stuck with the same branding and idents for say, 8 years and just
left things alone
, people might start to like them.

The brand seems too confused and unsure of itself because they keep messing things around all the damn time. How can they expect customers to have confidence in the brand.
However why keep a brand for 8 years if the audience and direction of the channel changes. America likes to stick to core brands much more so than Europe, which like to have more progressive branding which evolves over time.
You can argue that the content of a channel is more important to a consumer than the brand, especially with programmes shown individually on-line, and so its about showing the public the content you have first, and where to get it second, and some shows like Frasier, Scrubs, are shown on 3 or 4 different channels so how do you attract viewers then.
I think a 3-5 year cycle is healthy in some ways, especially with the change in technology and pace, just look at iPlayer, 2 years ago it didn't exist, so if we had an 8 year cycle, it wouldn't keep up with the times.
Sky have always focused on the content you get with sky, so its their brand, on images/video of the programmes, sports, movies etc, and a small channel identifiyer at the bottom. As the content shifts, the channel brands need to keep up, but the company brand hasn't had to. Now it has been over 10 years now since sky went all digital and brought in their current branding. Internet was just getting going, no video on demand or digital downloads etc, so the fact the brand is still fresh (following the glass refresh of 2004) is a testiment to the company, but in that time the channels have moved on time and time again.
Sky are now trying to reposition themselves away from a purely technical brand, satellite is now almost as prolific as Terrestrial and much more so than cable, so positioning yourself as the most technically advanced company isnt going to push the company forward. It is now moving to make itself as trusting and a softer reliable brand, as the BBC is viewed with public affection.
Maybe this softer approach will move into its channel brands, I don't think so. But the name sky has been enough to carry these other channels through, and if the channel brands adopt the new sky master brand, it should do it in sympathy with the channel's focus and audience, and not be thrust upon it in the ways prior to 1998. Sky 1, Sky Arts, etc appeal to different people, so why should their idents look the same?