It depends what the etymology of the name is. If (as I think I recall) the
second element is Greek _kleis_ 'key', then the family name should be
"Pteroclididae" or "Pterocleididae".
In the case of _Pterocles_, I believe the second element actually comes from
the Greek _kles_ ('famous'; 'noted for') rather than _kleis_ ('key'). The
same element pops up in _Carcharocles_, a genus of very large (and very
extinct) shark. _-kles_ was quite a common ending for proper names in
ancient Greece: Sophocles, Heracles, Iphicles, Themistocles, Pericles, etc.
Thus, Fain and Houde are grammatically correct when they give the sandgrouse
family as Pteroclidae, as given by Sibley and Monroe (1990-93), not
Pteroclididae. (Similarly, in Greek mythology, the descendents of Heracles
were called the Heraclidae.)
Alas, in this day and age, the grammatically correct version doesn't always
carry the day. We have Caudipteridae (rather than Caudipterygidae, as in
Archaeopterygidae) and Ceratopsidae (versus Ceratopidae, as in Meropidae).
There is also a family of sharks called the Megachasmidae (rather than
Megachasmatidae, as in Ctenochasmatidae). In recent decades, we have become
very sloppy in our naming conventions. Tut tut.