Negotiating often bears fruit at Khiva hotels. You’ll save money paying in som at the Orient Star and Malika hotels; at most others, it won’t matter. Only the Malika hotels, Asia Hotel and a few others stay open from December to February. In high season (April-June & Sept-Oct), it's a good idea to book ahead, or you won't be able to stay in the better options here, many of which are booked up weeks ahead.
Try removing some filters. Alternatively, there are some nearby lodgings with availability below.