Is it obligatory for a Muslim woman to leave a house in which objects appear and disappear in a manner that arouses suspicion and fear, despite her maintaining prayer and remembrance (dhikr)?

Your diligent observance of prayer and recitation of the Qur'an will protect you from ruin. If you are certain that items are disappearing from your home and no one has taken them, it could be the work of the Jinn. To remedy this, say "Bismillah" (in the name of Allah) when entering your home, when closing doors, and when placing things down, because the devil cannot enter or open anything over which the name of Allah has been mentioned, as stated in the Ahadith. If you still do not feel at ease after taking these measures, it is best to look for another home.