vsevolod4

Another tack you may want to try is instead of canceling, to change the booking. For this, you may need to contact the hotel reservations directly. Change it to a future date when you can use the rooms. This can work for "noncancellable" paid reservations as well, especially if you're a frequent guest and/or have status.
I wouldn't abuse this, but I've done this a few times (both free and prepaid reservations) due to flight disruptions; if the reason you're not there is you got stranded due to a flight cancellation/misconnection/etc., then they are likely to be sympathetic. But not the central reservation; this is at the discretion of the hotel. Some hotels, when you call them and ask for the hotel reservation transfer you to the central 800 number. Hang up, call back, talk to the front desk and explain your problem.
But if you knew it was noncancellable when booked, then you likely have no case. Or if it was cancellable up to 48 hours, and now it's 24 hours before, it's no noncancellable.

I also agree with other posters; I think the penalty for a "noncancellable" points reservation is that you lose the points; in this case 1 night.