Every time I try to go block a number on my Nokia Lumia 830, It says "That didn't work, though it's not clear why. Try it again." I have updated my phone to Windows Cyan, but this has been happening since the phone came out of the box.
If you have a Lumia 830 you probably mean you updated it to (full) DENIM.
You only can block a number which is in history of you phone or in other words the number must have called you before.
Is it also possible that your operator does not allow to block numbers or that you first have to call your operator to enable this feature?
If all of above fails you could assign a special ringtone to this number so you know it's this person.
Furthermore you could make a ringtone which has "no sound" so a silent ringtone in this case you even do not notice that you get this phone call.