How to update ios6 enterprise apps over the air

Yes, it is possible. When you deploy an Enterprise application it requires a plist that contains metadata about the application. This metadata includes the version number that you can use to check for updates.

BOOL updateAvailable = NO;
NSDictionary *updateDictionary = [NSDictionary dictionaryWithContentsOfURL:
                                  [NSURL URLWithString:@"http://www.example.com/pathToPlist"]];

if(updateDictionary)
{
    NSArray *items = [updateDictionary objectForKey:@"items"];
    NSDictionary *itemDict = [items lastObject];

    NSDictionary *metaData = [itemDict objectForKey:@"metadata"];
    NSString *newversion = [metaData valueForKey:@"bundle-version"];
    NSString *currentversion = [[[NSBundle mainBundle] infoDictionary] objectForKey:@"CFBundleVersion"];

    updateAvailable = [newversion compare:currentversion options:NSNumericSearch] == NSOrderedDescending;
}

Once you detect the update is available navigate the user to the download URL

itms-services://?action=download-manifest&url=<url-path-to-plist>

and it will install over the existing version leaving all data in-tact and even upgrade the CoreData database if you setup auto migration and make changes.

Thanks to Joe for a fantastic response. Here is the extended version translated to swift. You can put it inside of the viewDidLoad of your main view controller

let plistUrl = "https://example.com/example.plist"
let installationUrl = "itms-services://?action=download-manifest&url=https://example.com/example.plist"


override func viewDidLoad() {
    super.viewDidLoad()

    //Check for the updates        
    checkForUpdates()
}

func checkForUpdates() {
    let qualityOfServiceClass = QOS_CLASS_BACKGROUND
    let backgroundQueue = dispatch_get_global_queue(qualityOfServiceClass, 0)
    dispatch_async(backgroundQueue, {
        let updateDictionary = NSDictionary(contentsOfURL: NSURL(string: self.plistUrl)!)!

        let items = updateDictionary["items"]
        let itemDict = items?.lastObject as! NSDictionary
        let metaData = itemDict["metadata"] as! NSDictionary
        let serverVersion = metaData["bundle-version"] as! String
        let localVersion = NSBundle.mainBundle().infoDictionary!["CFBundleVersion"] as! String
        let updateAvailable = serverVersion.compare(localVersion, options: .NumericSearch) == .OrderedDescending;

        if updateAvailable {
            self.showUpdateDialog(serverVersion)
        }
    })
}

func showUpdateDialog(serverVersion: String) {
    dispatch_async(dispatch_get_main_queue(), { () -> Void in
        let alertController = UIAlertController(title: "New version of Example available!", message:
            "Example \(serverVersion) has been released. Would you like to download it now?", preferredStyle: UIAlertControllerStyle.Alert)
        alertController.addAction(UIAlertAction(title: "Not now", style: .Cancel,handler: nil))
        alertController.addAction(UIAlertAction(title: "Update", style: .Default, handler: { (UIAlertAction) in
            UIApplication.sharedApplication().openURL(NSURL(string: self.installationUrl)!)
        }))

        self.presentViewController(alertController, animated: true, completion: nil)
    })
}

Just distribute the update the same way you distribute the original. The user retains the data from the earlier version.