I would think they are open every day (with the exception of maybe big religious holidays).
Beleieve me, they heavily rely on the trade off the cruiseships to the extent that when we went back last Dec. (2004) a huge new pier had been built since the last time we where there back in 2000.
5 huge ships were in that day, the Carnival Victory, Carnival Glory, one Royal Caribeean ship and one Princess Ship with the Queen Mary 2 docked out at tender as the pier area was completely full.
I am sure if the ships are due in, the shops will be surely open!!!! Have a nice time, St. Maarten is excellent for shopping especially if you know what you are looking for.
My husband is a professional photographer using Canon gear. He knew what he wanted and haggled big time. In the end, he purchased $4,000 worth of Canon camera equipment for $1,900. In the U.K. that very same equipment would have cost him more like £4,000 and at the exchange rate we had that day (1.9 to the £1) that is over $7,000 so a HUGE saving.
Also the guy in the Camera shop was impressed because he was dealing with somebody who knew exactly what they were about - it was fun and hubs was over the moon.
Be aware though, there is a lot of building work going on within the shopping area at the moment so watch your feet - rubble everywhere but the shops are excellent value as long as you know what you are buying.