iOS: Can’t save file to ‘Application Support’ folder, but can to ‘Documents’

In case anyone is unsure how to do what rmaddy describes:

NSString *appSupportDir = [NSSearchPathForDirectoriesInDomains(NSApplicationSupportDirectory, NSUserDomainMask, YES) lastObject];
//If there isn't an App Support Directory yet ... 
if (![[NSFileManager defaultManager] fileExistsAtPath:appSupportDir isDirectory:NULL]) {
    NSError *error = nil;
//Create one 
    if (![[NSFileManager defaultManager] createDirectoryAtPath:appSupportDir withIntermediateDirectories:YES attributes:nil error:&error]) {
        NSLog(@"%@", error.localizedDescription);
    }
    else {
// *** OPTIONAL *** Mark the directory as excluded from iCloud backups 
        NSURL *url = [NSURL fileURLWithPath:appSupportDir];
        if (![url setResourceValue:@YES
                            forKey:NSURLIsExcludedFromBackupKey
                             error:&error])
        {
            NSLog(@"Error excluding %@ from backup %@", url.lastPathComponent, error.localizedDescription);
        }
        else {
            NSLog(@"Yay");
        }
    }
}