From the Hilton Diamond Benefits section. Read the fine print about Extraordinary Demand Dates. I'm not sure how you find out what the "specified days" are but I suspect it's by calling.

"Guaranteed Reservations availability: Reservations availability is guaranteed to Diamond VIPs when reservations are made before midnight hotel local time, 48 hours prior to intended arrival. Guarantee applies to only one room occupied by the Diamond VIP member and to reservations made with a valid credit card. Please note that this guarantee does not apply to rates - if a rate for which you are normally eligible is not available, your reservation will be subject to the hotel's prevailing rate for the accommodations requested. Please also note that in some instances, the guarantee may be subject to booking conditions such as length of stay requirements. Also note that in the event you do not arrive as scheduled and do not call to cancel and obtain a cancellation number, your credit card will be billed for one night's room and tax. Additionally, the reservations guarantee is not available during specified Extraordinary Demand Dates at certain hotels and is not available for reservations booked online. To make reservations under the Diamond VIP reservations guarantee, please contact our Diamond VIP desk at 1-877-4HHW-VIP in the U.S. and Canada. Outside the U.S. and Canada, call the Hilton Reservations Worldwide office nearest you. "