How to tell if gender dysphoria will persist? The only way to tell is to observe the individual over time. For it to qualify as a gender dysphoria diagnosis, the individual needs to have it for at least 6 months.
The focus of the gender dysphoria diagnosis is the person's reaction to both his/her physical anatomy and the societal prescribed gender role. At this juncture, we can look at the diagnostic criteria that are listed in DSM5. The salient feature is that there is a marked incongruence between one's experienced/expressed gender and primary and/or secondary sex characteristics. The person has a strong desire to be rid of one's primary and/or secondary sex characteristics as a result of a marked incongruence with one's experienced/expressed gender. They also have a strong desire for the primary and/or secondary sex characteristics of the other gender.
It is harder to make such a diagnosis in children and adolescents as their sex characteristics are still developing and it is hard to anticipate their reactions to them.
Clinically, it is crucial to distinguish gender dysphoria from an underlying psychotic disorder. I have come across patients who have psychosis and in their acutely psychotic state, they would hear voices (auditory hallucinations) advising them to under sex change operation. When the voices ceased, the persons are actually comfortable with their gender and has no gender dysphoria.
There are also people who cross dress to obtain sexual gratification. These people are usually comfortable with their gender and do not have gender dysphoria.