I had this one time on I think it was on approach.  I think it was the FMC telling auto throttles to be in approach mode making the aircraft incredibly slow.  I tried dumping fuel, but didn't have the time to verify it was working or not, as I just wanted to keep the aircraft from stalling.

I'm somewhat of a hack while flying, so probably I was doing something wrong.

I think I see the problem...go into the CDU, click on LEGS.  On the right half of the CDU is the miles to next waypoint, then underneath is a three digit number with a slash (/) then another number.  These two numbers are speed and altitude to cross that waypoint at.  I was showing 145/1700.  Maybe I was too heavy (still had 60,000 pounds of fuel left) at that point, so stall speed was right there. 

The best thing to do is select the approach, check it (speeds and altitude).  145 is incredibly slow for an air traffic controller (and obviously near stall speed for this aircraft), I'm thinking 180 or better  as you turn final (as long as you don't have a close turn on final like JFK 13R) would be best for them and you.

I just remembered, I am still on the CS AIRAC, I wonder if a newer one would be better?