I reckon it's often the third film that loses it. The second film generally has a lot going for it. A bigger budget because the first film has proven the concept. The original talent is still around and interested. The writers and director have idea that are either left over from the first film or they came up with too late to include in it. Second films sometimes get bad reactions because they are less original than the first, but judged on their merits they are often good.
By the third film, you've used up the good ideas. The genre becomes formulaic, with the formula defined by the elements that are common to the first two films. The original talent and writers have lost interest and moved on. There is no longer any real artistic drive behind the film. Instead, it's all about the money. The film is made to exploit the fans of the first two films. The budget will probably be higher, with more SFX, but no soul.
Obviously not all 3rd films are like this, but I think a lot are. With Hellraiser, for example, I like the second film because it takes the genre in a new and interest direction, with a visit to Hell, leviathan, exploration of what cenobites are and where they come from etc. It also keeps the same lead actress. The third film is formulaic. The chase across town, for example, is by the numbers. We have new cenobites with moving parts embedded in them, which wasn't technically possible for the earlier films, but they too are formulaic. If I tell you "Camerahead", you can pretty much imagine the monster even if you've never seen him. We even have a heroine with a boy's name. I agree the 4th Hellraiser film was atrocious, but for me the rot set in with the 3rd.
Alien 1 and 2: good. Alien 3: not so much. Blade 1 and 2: good. Blade 3: not so much. Terminator 1 and 2: good. Terminator 3: not so much. I've not seen T4 but maybe it follows the Hellraiser trend.