How to hide views UI reaching number of limits of searches
You can Set a configuration variable for each user (it's equal variables on drupal 7 ) and for each search increase it,reset it each day,But another and simple method is  implement it by cookie , create a cookie for user, set expire to 24 hours, and every time user search, first check it's cookie and if not do it more that three times  show results for him/her else  there is nothing to him/her.I think cookie solution is good for you.