I had this exact problem awhile back with an iOS app. Luckily, Apple has a nice form available for submitting a copyright dispute[1]. Long story short, I got paid. Just remember, you retain any code you own until it is signed over to the client. Especially for iOS dev, when someone gets an email from Apple legal, they tend to pay up.
While it is true you retain copyright on code you write until it has been assigned in writing (US copyright law stipulates that it can not be assigned verbally.) However, the situation may not be completely clear, unless you have been very careful you have probably given them an "implied license" to use your code.
I'd say an "implied license" would be contingent on payment. eg, if you verbally agree to let them use the code and quote them a fee, failure to pay the fee should definitely disqualify from that "implied license".
Same way as if I pick up a copy of windows from a shop without paying or figure out a way to download a valid windows license without paying - I don't have the license as I never actually paid for it, regardless of any agreements Microsoft might have written in the box about the license.
[1] http://www.apple.com/legal/internet-services/itunes/appstore...