Yes, its normal for KH to drop just like pH during a cycle. You'll probably need to either do some large water changes like MW said, or possibly resort to baking soda if the water changes are needed to frequently. Doing a few waterchange-recharge operations in the latter stages of a fishless cycle to kickstart it going again is not uncommon (people with softer tap water usually end up needing this more frequently, whereas people with relatively hard water can often get through the whole process without a water changes.)
When you do your water change its good to do it just like you will do once you have fish, ie. make it a full gravel clean during the water change. That will remove more debris and nitrates that if you just changed water without stirring up the gravel. If you want, test your nitrates shortly after the water change and if they're still high, do another one right away. Be sure to use conditioner and rough temperature matching for these water changes and then after the final one is done be sure to top your ammonia back up to roughly 5ppm and then wait an hour before doing another set of readings for your logbook.
~~waterdrop~~