I'm not sold that it means "difficult to exist/rare", instead of "there is a difficulty." It makes sense to think of thanking somebody as also apologizing for having them deal with a difficulty.
The eveidence presented on Wikipedia does not convice me. Even if arigatashi existed before contact with the Portugese, arigatō may have been a merger of obrigado and arigatashi.
On the contrary I feel the evidence is pretty much conclusive. arigatō comes from arigataku (an adverbial form), through a well-known "u-sound" change, as also explained on the page. Influence from Portuguese was not needed for that to happen.
Given the inflection exists for other words, e.g. o-medetaku -> omedetou and o-hayaku -> ohayou, I'm pretty sure it's derived entirely from Japanese grammar.
Modern Japanese -i adjectives formerly ended in -ki for the attributive form. This medial /k/ dropped out during the Muromachi period, both for the attributive form (-ki becoming -i) and for the adverbial form (-ku becoming -u). However, the adverbial form reverted back to -ku thereafter for most words, with the -u ending persisting in certain everyday set expressions, such as arigatō, おはよう (ohayō), or おめでとう (omedetō), and in hyper-formal speech.[4]
Also, no evidence of aigratou being used in the -u from before the Portuguese arrived. It may be true that the similarity is purely a coincidence, but the evidence is very weak, and maybe without Portuguese influence ariɡatau would be used only in some fringe cases.
