As already stated, stainless steel is bad about work hardening. This tends to be caused by feeding too slow, or a sloppy setup that allows chatter or hammering. A rigid setup and steady in feed will fix the problem.
I tend to disagree with the suggestion to use a carbide drill bit. I only ever use carbide drills in production drilling of plastic, aluminum and bronze because these are abrasive applications and tend to be lower strength materials. 304 doesn't dictate carbide, and the processing window would be narrower.
An ordinary HSS drill bit (not carbide, or even necessarily cobalt HSS) should be able to drill hundreds, perhaps thousands, of holes in 304 without a problem. Coolant helps because the heat conductivity of stainless is poor, power feed helps because the chip thickness window is more narrow than most materials and it prevents overfeeding during exit, a rigid setup helps reduce shock to the cutting edge and work hardening, and moderate surface feet per minute speed is important.
One of the most useful things folks on this forums could add to their drill press, band saw or mill is flood coolant with a recovery tank and pump. Then flood coolant (which is just water with some rust preventatives, frequently with cutting aids added) could be used to prevent the need to retract from the cut.
I wasn't aware that 303 was more scratch resistant and less gummy than 304.... I just thought it was just more free machining. I know 303 costs a good bit more. 304 is fairly soft but has very good corrosion resistance, particularly red rust resistance. 304 also welds nice. I have never had any problems machining it, even on older lighter machines.
Mete,
I think, for me, the single biggest pill in machining to date has to have been that tang you had me modify. I have filled up entire gaylords with chips from a days machining, but that thing took most of a day to make a small handful of tiny chips. That was some kind of stainless wasn't it? heh.