Can stainless steel rust? If not, why not? I believe it
can, from past experience; but perhaps I was misled into
believing the steel was stainless.
Yes, it can. It just takes longer than non-stainless.
Thanks. Why does it take longer?
It depends on the grade of stainless. There are hundreds of them.
http://www.principalmetals.com/properties/step2.asp?Family=Stainless+Steel
Stainless steels are any steel which contains more than 10.5% chromium. Cromium in alloy with iron causes the iron to rust less and rust slower, though I’m really not sure how, as I’ve recently failed chemistry. 
But they can still rust.
The Net is your friend
http://www.huber.de/edelstahl/roste.htm
http://www.mcnallyinstitute.com/04-html/4-1.html
http://mwb.brewer.net/KettleCare.htm
Over time stainless steel will typically begin to rust in tiny “pit” areas where the alloy mix is not optimal. If not stopped in some cases this “pitting” can spread and as the alloy oxidizes in these areas, compromise the stainless quality of adjoining areas.
Basically, rust is oxidation. All metals oxidize except inert ones like gold. If a metal can form a stable oxide, then the oxide layer prevents more oxygen from reaching the metal and causing more rust [oxidation]. In general a chromium oxide keeps oxygen form diffusing though to cause further oxidation. Normal iron oxide lets oxygen go though to continue oxidizing the steel so it keeps rusting. So if you have enough chrome, you will get a stable oxide film and rusting will stop. If you break up that oxide layer, the chrome steel will continue to rust.
Yes, stainless rusts.
When I was in the USAF, there was a contract let to replace to water pipes in the base hospital. It was decided that stainless steel pipes should be used instead of cast iron pipes. The contractor was careful, and put the pipes under pressure as each section was installed (parallel to the old cast iron at first) to check that there were no leaks. After a while, Civil Engineering (where I worked) started to get calls from the hospital that there was water leaking in the hospital. We went and checked and, sure enough, there was water dripping from the new pipes. WTF? We went over everything that could be reached without tearing open walls or floors, and found no leaks at the joints and no visible holes or rust spots. There was just water appearing on the outside of the pipes and no source we could find. It wasn’t condensation, either. We finally found a place on one pipe where there was an identifiable leak, and had it pulled out and examined. The area around the leak had miniscule pinholes through the pipe. They weren’t straight through - they zig-zagged through the pipe wall. We got in touch with the pipe manufacturer adn told him the whole story. They told us that you shouldn’t let water stand in stainless pipes for any length of time. It doesn’t rust through or get surface rust like regular steel or cast iron. It rusts along the weak areas where the alloy mixture isn’t perfect and develops the hairlines we had found. Somehow (this was never clear to me,) flowing water doesn’t do this to the pipes - perhaps the dissolved oxygen in the water doesn’t have time to react. At any rate, stainless rusts, but you don’t necessarily see it as surface rust and a piece of stainless might be completely sponged with rust and weak as a piece of rotten wood without looking that weak. The contractor ended up replacing all of the stainless at his cost, and this time he didn’t leave water standing in the pipes.
A useful tool that scuba divers carry is a s.s. knife. THere are really 2 grades one is 405 ss the other is 354 ss? well 35something. The 405 is stronger but has to be oiled after each exposure to water as it will start rusting (not pitting - but real rust). The 35x ss knives are weeker and could bend if you use then for prying but don’t rust (maybe they will pit given enough time)