Moving an object randomly around the screen

try this:

    -(void)animationLoop:(NSString *)animationID finished:(NSNumber *)finished context:(void *)context { 

        [UIView beginAnimations:nil context:nil]; 
        [UIView setAnimationDuration:1]; 
// remove:
      //  [UIView setAnimationRepeatCount:1000]; 
      //  [UIView setAnimationRepeatAutoreverses:YES]; 

        CGFloat x = (CGFloat) (arc4random() % (int) self.view.bounds.size.width); 
        CGFloat y = (CGFloat) (arc4random() % (int) self.view.bounds.size.height); 

        CGPoint squarePostion = CGPointMake(x, y); 
        button.center = squarePostion; 
// add:
     [UIView setAnimationDelegate:self]; // as suggested by @Carl Veazey in a comment
        [UIView setAnimationDidStopSelector:@selector(animationLoop:finished:context:)];

        [UIView commitAnimations];
    }

and just add a counter (int) inside the method to check if it's executed more than 1000 times, if wanna stop it...