This petition was rejected

The Government e-Petitions Team gave the following reason:

We can't accept your petition because we aren't sure what you mean by acknowledging vestibular conditions as a chronic disability.

Laws and policies, including the Equality Act and the PIP assessment process, don't list specific conditions and define them as disabilities. In most cases, it’s the impact that a health condition has on the person’s life that qualifies them for support or protection under the law.
 
You can find out more about showing that you're disabled under the Equality Act here:  

www.citizensadvice.org.uk/law-and-courts/discrimination/protected-characteristics/showing-you-re-disabled-under-the-equality-act/

You could start a new petition calling for a Government funded campaign to raise awareness of vestibular conditions if that is something you would like to see happen.