I don't know...I never really thought about the seems-dead-but-isn't thing before. However, I would argue that Gandalf should be excluded from the category, because of them all, he is the only one who actually died, as in really wasn't alive any more.
I believed it just about every time. Others have said that they began to suspect something was up by the time Pippin's turn rolled around...but my most distinct memory of my first time through the books was that upon reaching the end of The Black Gate Opens, I actually refused to read more, and cried myself to sleep that night. Gullible? Yeah. But I was only 13 at the time, and was running on very low sleep and high adrenaline (reading LOTR still does that to me). The strange thing is that I never believed for a moment that Eowyn was dead. It always looked to me like a rash misdiagnosis on Eomer's part, partially influenced by his grief over Theoden, rather than an actual death...And it turns out that's exactly what it was.
I don't see the frequency of these incidents as a flaw. It's a book that tells the tale of a war. People die in war (like Halbarad, Boromir, Theoden, and countless others). People get hurt, too. But we have to take into account that to a person living in Middle-earth, a badly hurt person may in fact appear dead. Medicine wasn't advanced enough for them to tell the difference between coma/unconsciousness and death. (As a morbid side-track, when people excavated midieveal cemetaries, some of the coffins they found had scratch marks on the inside of the lids) Sam, who doesn't think best with his head, and knows absoloutely nothing about medical stuff could easily believe Frodo to be dead. It's a mistake I probably would have made, had I been in his shoes. I see Frodo's "death" after the encounter with Shelob as an honest mistake on Sam's part...though one that is, of course, intended to play a bit with the emotions of a reader.
Anyhow,a lot of people probably looked dead that weren't, though I must say that among the Fellowship and their friends, the incidence of this is somewhat rediculously high.
The only "death" I see as more of a direct attempt to convince readers that it actually happened is Pippin's. It has a different feel to it than the others. Gandalf actually was dead, for however brief a time. Eowyn and Frodo, and I guess we can include Merry in this one, were more of a misunderstanding by a character, than anything else. Readers make the mistake of belief along with the characters. Pippin's death is different, because it's only what Tolkien tells us of Pippin's own thoughts at the time of his injury. We don't get that particular window into a character's soul for any of the other "deaths" we experience in the book. I'm trying to say something here, but I can't think of the right words, so I hope you get it.