With a DPE you would have to appeal with the FSDO that provides DPE oversight in that region. I’m not sure what the time frame is but I expect it would have to be the very next workday if not immediately.
A FAA inspector may decide to re-examine you if grievous actions on the part of the DPE caused the fail.

Like what I should have done in the case of one of my students long time ago.
Student made it to the airplane and the starter failed upon which the DPE decided to give him a pink slip because he was “weak on the oral anyway”. So why didn’t you fail him then?
He should have been issued a discontinuance, that’s specifically what they are for.
Anyway I was weak and didn’t want to make waves so I didn’t appeal it just verbally protested with the DPE in question who lost his designation about 10 years later.

Now saying that you weren’t out of tolerances on a maneuver is going to be impossible to prove. A DPE can also set an intimidating atmosphere which will lead to a fail, now this may be intentional but again very hard to prove.
Forcing an applicant to fly in clearly unfavorable conditions is another one.
Now this is a tricky one as you can be reasonably expected to handle some less then ideal conditions as you should have been exposed to those during training.
However gusting 25 for a Private pilot applicant is too much AMS that is why you should be available for your student during their check-ride and you as the instructor should pull the plug on a ride and take the possible backlash.