You cannot save anything inside the app's bundle, but you can use +[NSData dataWithContentsOfURL:]
to store the image in your app's documents directory, e.g.:
NSData *imageData = [NSData dataWithContentsOfURL:myImageURL];
NSString *imagePath = [[NSSearchPathForDirectoriesInDomains(NSDocumentDirectory, NSUserDomainMask, YES) objectAtIndex:0] stringByAppendingPathComponent:@"/myImage.png"];
[imageData writeToFile:imagePath atomically:YES];
Not exactly permanent, but it stays there at least until the user deletes the app.