FATAL: Thread create failed: Cannot allocate memory

[Phil Mayers]

We had one of our MAC-auth radius server instances hang up with this
error at about 0200 this morning.

That server receives pretty heavy load, and it's bursty, so we see this
a couple of times a day:

The maximum number of threads (32) are active, cannot spawn new thread
to handle request

...but it does not cause problems. An inability to create a new thread
is an entirely different matter though; it implies <max threads are
running, the server tried to create a new one, and the OS couldn't
allocate a thread.

Any ideas how to resolve this? Version is FreeRadius 1.1.6 (only reason
we haven't upgraded is change control, it's due shortly)