NON EU,UK BORN BABY DOES NEED A VISA?

Hi friend
I applied T1 Entrepreneur in 2013 with 2 dependents (Wife and 1 year old son).
Application was refused and was in court till November 2015.
In January i applied again T1 entrepreneur with my depended wife (not applied for my son).
I consult with few lawyers and they said that baby is born in UK, he doesn't need a visa unless he travel outside UK, so dont apply for baby.
I received a confirmation of application from HO and Biomatric letter as well.
i gave my bio metric with my wife 10 days ago.
Today i received a letter from HO and they asked, why you did not apply for your son, our record shows you applied last time.
They gave me 14 days to give them solid reason, why i did not apply for my son.
please share your valuable views and advice me.

Kind regards

If baby, who has never applied for any leave, is not travelling, then leave to remain is not normally required.

However, if son was previously granted leave, then he should continue to extend, probably quoting A280(b), 304-309 (as 319H(m) may fail), else he may be an overstayer.

But after you are granted ILR, your UK born child will be entitled to register for British citizenship directly. The overstay won't matter, if child is under 10 years old.