"Inimpugnable" means that it can't be disputed; "impugnable" means that it can.

It seems that non-impugnable doesn't exist in English, at least for practical purposes; I can't find it in genuine EN legal texts, and I certainly haven't encountered it before. The appropriate term, I believe, is "unchallengeable" or "non-appealable"; I think either would do here. Both can readily by found in this sense (try googling them).

This may well be from Peru; I find this form of words in documents from there relating to public tender processes:

"Un aspecto importante que debe tenerse presente es que de conformidad con lo dispuesto por el literal j) del artículo 51.1 de la NLCE, se considera una infracción interponer recursos impugnativos contra los actos inimpugnables, sancionable con inhabilitación temporal para contratar con el Estado por un periodo no menor a un (01) año ni mayor a tres (03) años."
http://www.osce.gob.pe/consucode/userfiles/image/LAS IMPUGNA...

This document explains in detail which "actos" are "impugnables" and which are not.

"Infracciones que ameritan instauración del procedimiento sancionador (art. 237)
j) Interpongan "recursos impugnativos" contra los actos inimpugnables establecidos en el Reglamento"
http://es.slideshare.net/calacademica/27-11-procedimiento-ad... (slide 11).

So challenging or appealing against unchallengeable or non-appealable decisions will not only fail but is actually a proscribed practice subject to sanction.