Any ideas? I find often my characters either reach the solution immediately, or get stuck and I can't unstick them. Or I get myself confused and have a mess that makes no sense.
Try making them reach the wrong conclusion first or, perhaps, encounter some kind of obstacle when they are about to find a key fact.
I suppose it depends on what kind of mystery you're writing, but I'll assume you're looking at an Agatha Christie style, old fashioned murder mystery. Like Racktash says, red herrings and obstacles are your friend. If there are false clues, or clues that are interpreted the wrong way, that keeps the suspense building while the detective is running around trying to connect the dots. Throwing in obstacles to overcome (someone warning him off the case, a brand-new murder when he is interrogating his prime suspect, losing his lucky pen) keeps your story moving and fresh. Your characters should only know what they can see, so if someone wears a feather boa, and a feather is found at the scene, they become the immediate suspect, since no one knows that Old Man Jones likes to go feed the peacocks on the other side of the estate. Personally, I would think that if YOU don't know who the murderer (or whatever) is until the end, that might help a bit. Maybe pick two characters as your prime suspects, set them both up with some clues (or clues that could point to either), and figure out which one of them is actually guilty when you get there. It might not work, might just make it muddled, but it's worth a try, no?