Apologies if the following post is a bit technical, but sometimes I have to let the nerd loose.
Growing up, I was always taught that the staccato-under-a-slur was a sort of "longer staccato," about 3/4 length or so. More recently, after studying Baroque and Classical performance practice, I've come to understand that this marking actually refers to a very intense legato. The notes should be held as long as possible, lingering on each one to create a sense of urgency or longing. Here are a couple of examples where this interpretation makes sense:
Reynaldo Hahn's exquisite chanson "A Chloris" references Bach's famous so-called "Air on the G String" throughout the piece, until this point (end of p. 61, beginning of p. 62). In context of the piece, suddenly shifting to a detached texture would be jarring, and break up the beautiful long lines that fit the text of this song so well.
The slow movement of Mozart's B-flat sonata, K. 333 contains several portato markings. Invariably they lead into an expressive leap or harmonic shift, so it makes good sense to play these figures with heightened intensity. They would sound somewhat trivial if they were detached.
If you really want to blow your mind, take a look at the Liszt Sonata and you'll find countless portatos (portati?), particularly in slower, more expressive moments. Playing these figures in a detached manner would be, frankly, ridiculous.
Why the shift in interpretation, then? What made us go from "intense legato" to "long staccato?" Perhaps as a result of increased specialization among classical performers, we lost sight of the context of our notation. Slurs for keyboard were originally borrowed from the string world, so an "intense legato" corresponds to more pressure on the bow, for instance. Shorter slurs in the Classical repertoire are analogous to bow changes, which should create small, but noticeable, articulations between the slurs.
Anyway, enough for now; I'll try to come down from the ebony-and-ivory tower a bit next time.