I'm a little curious about something - how rare is it for a cat to be
sterile on birth?

I ask as one of our girls at eight months has shown no signs of going into
heat.  (Yes, I know, get them fixed - this is soon to happen.)  To note,
her medical history has her nearly dying of a resp infection this past
November, and was on antibiotics (Clavamox and one other one, some pink
liquid I can't remember the name of) and nebulized as part of the
treatment.  (Thrown in - I've heard that sometimes this sort of thing can
coincide with sterility.)

She's otherwise a perfectly healthy (though non-standard colored) bengal
kitty.  (Recent pics to show Real Soon Now.)