Just because some tool shows availability does not mean there actually is availability for your specific itinerary.

1) The tool you use could be using a GDS that is not native to the airline, and thus not up to date.

2) Some airlines (including SQ) restrict availability based on point of sale (ie they prefer expensively bought Z class over cheaply bought Z class). Some availability tools are based on a certain (normally US) point of sale. Others allow the user to select the point of sale.

3) Some airlines may restrict availability based on fare within a booking class.

4) Married segment logic commonly applies. This is where availability is apportioned between origin and destination pax (O&D) and connecting pax. There are all sorts of reasons for this - eg to make their schedule work more efficiently, to maximise revenue, to reduce risk of delays, etc.