Many luck egalitarians argue that social institutions should prioritise neutralising the disadvantages people face which are a result of unchosen social or natural causes, over disadvantages caused by individuals' own reasonably avoidable choices. One of the main objections to luck egalitarianism is known as the Abandonment Objection, which argues that luck egalitarianism is implausibly harsh towards people suffering as the result of their own choices. I consider a number of luck egalitarian responses to the Abandonment Objection as applied to health care, and argue that none of these responses adequately answers the challenge of the abandonment objection while retaining the importance of key luck egalitarian principles.