How is a kohen demoted in terms of “losing his kehuna”? generally, a kohen who does not abide by the torah restrictions placed on kohanim is only temporarily demoted until he chooses to resume following those rules.

In terms of a third-party wishing to disprove a kohen’s status as kohen, things get difficult if not impossible;

The mishna relates that as long as there aren’t “עוררין” to challenge the kohen’s ancestry, one kosher witness is sufficient and believed to the authenticity of the said kohen (Mishna, Ketubot 2:8).

The kosher challenge

What is עוררין though? translated as “claims of complaint/dissatisfaction” the rambam details it as two kosher witnesses claiming that his ancestry contains a challal.

When there are indeed עוררין that the kohens ancestry is tainted, those witnesses are evaluated by בית דין and challenged thereby as their testimony negates the chazaka of this individual as a kohen.
The tosefta relates what is NOT a valid disproof, for example if one says “how did this guy get bumped up to kohen status as he’s never gone up for ברכת כהנים in his life” -this isn’t deemed a valid disproof (tosefta כתובות ב ח).

No chazaka in your family? you may not be a kohen

There has been instances where a thought-to-be-kohen, with little or no chazaka, has been absolved of being a kohen in the first place. These cases include a child adopted by a kohen and his wife who assumed his stepparents family name such as “kohen” or “katz”, family’s who last name where shortened to katz from ketzenellenbogen or a jew with the family name “kaplan” being told that all kaplans are kohanim.

These are some examples of a feeble foundation to kehuna and need to be independently verified on a case by case by an orthodox rabbi competent in dinnei yichsei kehuna (the halachic laws of kehuna heritage).