If you go to Madrid's Palacio Real's official website @ http://www.patrimonionacional.es/ , click on the English version (if necessary), then on "Practical Information for Visitors" and then choose your palace and at the bottom click the OPENING HOURS you'll see that the Royal Palace is open Mondays all year 'round.

The tour is good but much shorter (and you see fewer rooms) that you'd think. But it's still something special to see/do in Madrid.

Saludos, MadridMan