the use of "shouldn't" is OK but perhaps not as common as using "wouldn't" So I prefer "I see no reason why it wouldn't work." Meaning: It should work and I don't see any reason why it wouldn't.

It means - it should work but they have used this phrase as an indication of "well why wouldn't it "

It may mean both. If you are trying to fix something and can't understand why it should work, but doesn't, then you can say this. I say it all the time! :) You can also say it if someone asks you whether or not something will work if they do it. It's a safer way of saying "Yes, it will work" without looking bad if it doesn't.