TextViewInUIAlertController.swift

import UIKit

class ViewController: UIViewController {

    override func viewDidLoad() {
        super.viewDidLoad()
        
        let showAlertButton = UIButton(type: UIButtonType.Custom)
        showAlertButton.frame = CGRectMake(0, 0, 100, 40)
        showAlertButton.setTitle("Show Alert", forState: .Normal)
        showAlertButton.setTitleColor(UIColor.blueColor(), forState: .Normal)
        self.view.addSubview(showAlertButton)
        showAlertButton.center = self.view.center
        
        showAlertButton.addTarget(self, action: "showAlert", forControlEvents: UIControlEvents.TouchUpInside)
    }

    let alertController = UIAlertController(title: "\n\n\n\n\n\n", message: nil, preferredStyle: .Alert)
    let textView = UITextView(frame: CGRect.zero)
    
    func showAlert() {
        
        let saveAction = UIAlertAction(title: "OK", style: .Default, handler: nil)
        
        saveAction.enabled = false
        
        let cancelAction = UIAlertAction(title: "Cancel", style: .Cancel, handler: nil)
        
        alertController.view.addObserver(self, forKeyPath: "bounds", options: NSKeyValueObservingOptions.New, context: nil)
        
        NSNotificationCenter.defaultCenter().addObserverForName(UITextViewTextDidChangeNotification, object: textView, queue: NSOperationQueue.mainQueue()) { (notification) in
            saveAction.enabled = self.textView.text != ""
        }

        textView.backgroundColor = UIColor.greenColor()
        alertController.view.addSubview(self.textView)
        
        alertController.addAction(saveAction)
        alertController.addAction(cancelAction)
        
        self.presentViewController(alertController, animated: true, completion: nil)
        
    }
    
    override func observeValueForKeyPath(keyPath: String?, ofObject object: AnyObject?, change: [String : AnyObject]?, context: UnsafeMutablePointer<Void>) {
        if keyPath == "bounds"{
            if let rect = (change?[NSKeyValueChangeNewKey] as? NSValue)?.CGRectValue(){
                let margin:CGFloat = 8.0
                textView.frame = CGRectMake(rect.origin.x + margin, rect.origin.y + margin, CGRectGetWidth(rect) - 2*margin, CGRectGetHeight(rect) / 2)
                textView.bounds = CGRectMake(rect.origin.x + margin, rect.origin.y + margin, CGRectGetWidth(rect) - 2*margin, CGRectGetHeight(rect) / 2)
            }
        }
    }
}

It must removeObserver in saveAction and cancelAction of Handler.

alertController.view.removeObserver(self, forKeyPath: "bounds")