There are a number of things that can cause a 'brittle' fracture in SS. A couple of them are primary. One is the high volume percent of what is called sigma phase. This is a hard brittle intermetallic phase (composed predominantly of Fe, Cr, and Mo) that when present in high volume percents can impose its properties of brittleness upon the microstructure as a whole and manifest in mechanical testing or even in certain service regimes. This is a diffusion controlled process and is therefore related to time at temperature. This is why those alloys are particularly susceptible will require greater heat input control.
Then there is liquation cracking wherein low melt eutectics create a liquid film at grain bounderies and are not quite solidified at the very moment when tensile stresses created from weldment cooling are trying to pull the weldment apart.
Tis is also somewhar  related to star fractures or crater cracks wherein the 'junk' elements such as S and P are pushed ahead of the solification front to create high volume percents at weld stops.
Both of there phenomena can be related to overheating the alloy.
Hopefully Chuck will chime in here to help clarify some of these issues and add more.

As Jeff made some good points, and I agree, sigma is prevalent for embrittlement, but let me add just a little. I believe embrittlement is also prevalent in the martensitic, and especially the ferritic metals. The DBTT (Ductile to Brittle Transition Temperature) is especially noticed in the ferritic materials. In this sense, excessive grain growth will decrease the strength and toughness of the ferritic steels. Since most stainless steels do not have a problem with excessive grain growth, the ferritic steels are more affected. The ferritic structure is much more prone to grain growth than the austenitic and duplex grades. This, combined with the fact that the ferritic steels start out with a lower level of toughness makes them more vunerable to embrittlement in the HAZ. I hope I didn't totally miss the point...

Chuck