What are the limits of refraining from doing good deeds for fear of showing off?

Satan is keen on trapping a Muslim in one of two situations: either performing an action out of ostentation and seeking a reputation, or abandoning it altogether. The sincere Muslim is not concerned by Satan's whisperings and does not fear ostentation, for to a sincere heart, performing an action in secret is the same as performing it openly. Sheikh Ibn Baz was asked about a woman who feared advising others out of fear of ostentation. He replied that this is one of Satan's ploys to discourage people from inviting others to Allah. She must not pay attention to that, but rather advise, be sincere to Allah, and be truthful with Him. She should not abandon what Allah has obligated upon her out of fear of ostentation, in affirmation of His, the Almighty's, saying: "The believing men and believing women are allies of one another. They enjoin what is right and forbid what is wrong and establish prayer and give zakah and obey Allah and His Messenger. Those - Allah will have mercy upon them. Indeed, Allah is Exalted in Might and Wise." (At-Tawbah (definition)/71). Sheikh Ibn Uthaymeen mentioned that abandoning acts of obedience out of fear of ostentation is not correct. Rather, one must perform the act of obedience, but without having the intention of showing off in one's heart.