You don't need to do the animation with 0 duration when the object reaches the end of the screen. Just test for this in your completion block and relocate the view before calling recursively. Also, a duration of 0.01 seems a bit extreme (100 frames per second). Perhaps a more reasonable value like 0.1 would help.
Something like this:
- (void)effectOnObject:(UIImageView *)object{
//setted duration to short time
CGFloat duration = 0.1;
[UIView animateWithDuration:duration delay:0 options:UIViewAnimationOptionAllowAnimatedContent
animations:^{
NSInteger initialX = object.frame.origin.x;
//this change the speed of object
NSInteger initialy = object.frame.origin.y + 10;
[object setFrame:CGRectMake(initialX, initialy, object.frame.size.width, object.frame.size.height)];
}
completion:^(BOOL completed){
NSInteger initialX = arc4random() % 321;
//generate random position to relocate the object on y axis (little bit above top of screen)
NSInteger initialy = ((NSInteger)-object.frame.size.height) - arc4random() % 11;
[object setFrame:CGRectMake(initialX, initialy, object.frame.size.width, object.frame.size.height)];
//recursively call
[self effectOnObject:object];
}];
}