performSelector:withObject:afterDelay: not making call

I ran into this same issue, and by necessity I solve it slightly different from the accepted answer. Notice I wanted my delay and selectors to be variables? Using a block allows me to stay within my current method.

dispatch_async(dispatch_get_main_queue(), ^{
       [self performSelector:loopSelector withObject:nil afterDelay:cycleTime];
});  

By the way, this is definitely a threading issue. The documentation for performSelector:withObject:afterDelay: states that this will be performed on the current thread after the delay, but sometimes that thread's run loop is no longer active.

A more detailed discussion on the subject can be found here

Try using:

-(void) select {   
    [self changeButtonNames];
    [self drawMap];
    [self performSelectorOnMainThread:@selector(showActionSheet) withObject:nil waitUntilDone:YES];
}

-performSelector:withObject:afterDelay: schedules a timer on the same thread to call the selector after the passed delay.

Maybe this will work for you:

-(void) select {   
    [self changeButtonNames];
    [self drawMap];
    [self performSelectorOnMainThread:@selector(someA) withObject:nil waitUntilDone:YES];
}

-(void)someA {
    [self performSelector:@selector(showActionSheet) withObject:nil afterDelay:2];
}