I don't think I ever get special challenge notifications. I just check on the 1st day of the month for available achievements. If you miss meeting the goal required -- sometimes daily goals, the achievement for the month disappears as it is no longer possible to meet the required stats to achieve the medal. For example, my special challenge for June is to double my move goal every day. If I had missed doing that on the 1st day of the month, the special achievement for June would have disappeared.
Sometimes when I read that people haven't received special achievements, I wonder if it's because they check after the 1st day of the month, and they've already not met the required stats to keep the achievement visible for the entire month.
Also, to make sure I see the special achievement for the month on the 1st, I reboot (slide off) my phone and watch on the 1st day of the month.