What is the Biblical basis for saying one won't be healed if they lack sufficient faith? I've heard it said in discussion with teachers in a Pentecostal church, "If you pray and believe, God will heal you." The teaching seems especially motivated by passages like Mark 5:34 and Mark 10:52 that quote Jesus saying, "Your faith has healed you." One member of the church was even later heard saying, "I prayed for healing, but I wasn't healed because I didn't have enough faith."

What is the Biblical basis for the proposition, "If you don't have enough faith that God will heal you, then he will not heal you"?
Great question. I found a few scriptures that partially satisfy your parameters, but the only one that really suggests that miracles/healing were adversely affected by a lack of faith is below:

And when the sabbath day was come, he began to teach in the synagogue: and many hearing him were astonished, saying, From whence hath this man these things? and what wisdom is this which is given unto him, that even such mighty works are wrought by his hands?
Is not this the carpenter, the son of Mary, the brother of James, and Joses, and of Juda, and Simon? and are not his sisters here with us? And they were offended at him.
But Jesus said unto them, A prophet is not without honour, but in his own country, and among his own kin, and in his own house.
And he could there do no mighty work, save that he laid his hands upon a few sick folk, and healed them.
And he marvelled because of their unbelief. And he went round about the villages, teaching. (Mark 6:2–6 KJV)