I believe this is probably good reasoning. Looking at http://www.the-numbers.com weekend charts for 2008, here’s an armchair analysis…
Little Nicky’ #2 weekend debut came a week after Charlie’s Angels (which held #1 that second week). Just a guess, but I imagine the same crowd that likes Adam Sandler films probably also enjoys comedic action with T&A. At debut, per theater earnings were 30% less than those for CA, and about 10% less than the #2 film, Men of Honor.
The very next week (dropping to #7), the year’s top box-office movie debuted: How the Grinch Stole Christmas. While appealing to families, it also is a Jim Carrey film that had a fair amount of puerile humor, which would appeal to the Adam Sandler crowd, sapping week-over-week take more than normal. Per theater earnings in week 2 were far below the six movies ahead of it, and nearly matched per theater earnings of the #8 film, Meet the Parents, which had debuted 7 weeks before.
In its third week, LN had dropped to #10, below the much older Meet the Parents, with per-theater earnings almost half of MtP’s earnings.
Looking at Adam Sandler film trends from the same site, he had released four comedies in fairly rapid succession before LN-- three in 1998, and one in early summer of 1999-- with the last two being >$160 million hits (The Waterboy and Big Daddy). Little Nicky took a year and a half to debut after the last one, so the studio lost the momentum of his brief spurt of popularity.
So, analysis: the fad for Adam Sandler films had faded, but expectations for performance were set too high. Sandler-friendly demographics went for Charlie’s Angels in LN’s debut, making Little Nicky’s take look anemic, so it was probably dubbed a flop by pundits. The low numbers would start to discourage advertising by the studio.
In its second week, getting drubbed by so many new-comers, and looking particularly weak against the other big box-office comedian solidified its reputation as a flop. Advertising would be minimal by now. Folks looking for a comedy (especially one whose theater would not be filled with children being dragged to the Grinch) would instead be drawn to Meet the Parents, which had good word of mouth, continued advertising, and was known as a hit.
Falling to #10 in three weeks showed that the film wasn’t going to be a sleeper, begin thriving on word of mouth, or be the go-to alternative for folks sick of family/Christmas films… Meet the Parents had that sewn up. By this point, the studios would be getting ready to release it into the second-run circuit.