how can an additional natural join with the same table twice *reduce* the row count

This is real results from my database. I spend some time trying to reproduce this behavior with an SSCCE but failed. How is the last of the below results possible?

SELECT COUNT(*) FROM rr.resource    a
--- 15771

SELECT COUNT(*) FROM rr.resource    a
NATURAL JOIN rr.interface   b
--- 41419

SELECT COUNT(*) 
FROM rr.resource    a
NATURAL JOIN rr.interface   b
NATURAL JOIN rr.interface   c
--- 0

The zero (0) row count in the last query is consistent and repeatable every time.
In some examples I created, adding a second natural join with the same table twice yields the same number of rows (as I was expecting). How is then the above result possible?