Is the fear that prayer will not be accepted due to a shortcoming in maintaining kinship ties considered a Waswas (a tempting whisper from Satan) or something praiseworthy, especially since the relative only contacts by phone on special occasions? And does the action of one who falls short in maintaining these ties become null and void?

Fear of severing ties of kinship is praiseworthy because it is a fear of committing a sin, but exaggerating it is blameworthy. The acceptance of prayer has no relation to maintaining ties of kinship. So, whoever performs a prayer that fulfills its conditions and pillars and performs it with devotion, Allah will reward him for it, even if he is one who severs ties of kinship. There is no evidence to prove that one who severs ties of kinship will not be rewarded for his prayers or good deeds.