When I try to take a picture using the timer, sometimes the indicator doesn't blink so I have to click the shutter a couple of times for it to start counting. Why is that? I'm using a Nikon D5200 with the 18-55mm lens kit.
It sounds like you are not waiting for the camera to get a focus lock before fully depressing the shutter - as per taking normal photos you need to HALF-depress the shutter, wait for focus (at your desired point) and then fully depress to start the timer.
If you are struggling to find a focus point at your desired distance, you could always use manual focus mode instead.