Changing the filing status shouldnt disallow EFiling.  Use the Review button and read the diagnostics, WHY cant it be EFiled? Is there an error somewhere?

Just a guess. Change back to MFS and delete the spouse, then change back to HoH and see if it clears the error. Another possibility is that as MFS there are entries tied to a spouse that need to be cleared.

Is this an amended return?  If so, what year?

As Lisa said, how exactly does it not allow you to e-file (if there is an error message or a rejection message, what is it)?

Yes this is an amended. And Error says: 

Thanks a lot Lisa, you are perfect.

Thanks, @Lisa and @TaxGuyBill and other folks to me  always helpful.

First I filed MFS and his daughter student under 24, she already filed as single and she was not  dependent for the client.

Now that I am going to paper file because of changing status 1040-X for client, E-filing for her daughter now is available as a dependent by 1040-X. ( single independent to single as a dependent)

can I E-file for daughter for today (before the IRS begins shot down E-filing) and for some reason paper file for the client by 3-4 weeks later, he is out of the country.