In the event of a Handling Agent being unable to make a profit on a particular airline, I would suggest there are two outcomes.
1. The airline is forced to up its offer or look elsewhere (Good for handling agent)
2. The airport authority steps in and subsidises an agent to do the work. (I think it'd have to be a significant airline for this to happen).
I have heard rumours of this happening a while ago at NCL with a certain high-profile charter company who were going to be agent-less. The airport couldnt afford to even think about losing the X-number of flights (and passengers) over the summer season and in effect paid some money to the agent and offered significant reductions in rent in order to ensure the airline remained flying. Not sure if this is standard practice or not.
RTG!