A beach resort hotel will normally put some std rooms into the award inventory AND they may also put in some rooms that require a per night co-payment or extra points per night. These "upgraded" rooms usually are ones that have a better view (i.e. ocean view, ocean front, etc), more space (i.e. corner room), balcony, or some other "upgrade".

The issue you may be finding is that Plats and Gold elites will quite often be upgraded to these types of rooms for free (if available at check-in.) Also, there may be others who just don't think the upgrade is worth the cost or needed. As such, most who make award reservations will go for the standard room that has no extra per night charge. When enough persons grab all the standard rooms in the award inventory, that leaves only the "upgraded" rooms available for awards. Your problem is May 21-26 isn't that far off and may very well be a high season for them (meaning a lot of people have already made reservations and there just aren't very many rooms left.)

You can try a couple of things:

1. Make a reservation with the extra charge and enjoy the upgraded room.
2. Make a reservation with the extra charge, but check back weekly or even daily to see if standard room availability opens up. If it does, call MR and have them change your reservation to one of the standard rooms that has no extra charges.
3. Call (or email) the hotel and ask to speak with the GM or one of the managers. Depending on the hotel's available unreserved rooms and your persuasiveness, you might be able to get them to give you a reservation with a standard room.
4. Change your travel dates to one where there is standard room award availability. If you can push your dates farther out, you may have better luck finding standard award availability.