I'll repeat my post from the 'Welcome Newbies' thread and add a bit (mods might want to sort this one out!)
You can't always solve every case. It's always better to quit rather than to guess and risk getting an expensive false accusation. We all have to quit cases sometimes.
Don't forget there are different ways of identifying the guilty party:
Physical evidence and fake/no alibi
Witness evidence and fake/no alibi
Two pieces of witness evidence
As you progress through the game you add to your skill set and equipment set, both of which help to avoid cases where everyone clams. Make sure you're not doing cases which are too hard for your current level. If everyone's clamming too quickly, try doing a few easier cases till you've gained better questioning skills and/or better gear.
Two other options, which may or may be available to you, are asking an agency mate to help you unclam a suspect or three (spoiler technique there, so I won't say anymore, sorry), and the use of the skill Surveillance. Neither option is guaranteed to work, just offers the promise of help.
And like Cordy said, no one here, regardless of how good their skills are, can tell you they can solve every case, every time.