I have been in the regrettable position where I have had to cancel courses right up to the point where they are about to start.
Such decisions were based on whether the course stood to cover direct costs (tutor fees, out of pocket expenses, accommodation costs, consumables etc.) rather than on their contribution to the overall budget (which is out the window anyway). In these cases, we would endeavor to ensure that the tutor, and in some instances the students, know of the risk of cancellation due to low recruitment and the deadline by which a decision would be made.
What puzzles me with your situation is that the course has already begun, therefore:
- Costs have already been incurred (in your time)
- Certain costs will already have been committed to (room bookings, catering etc.)
- Students will have paid fees (or have had their fees paid for them in whatever form)
If the course would be cancelled, fees would be refunded or lost (government funders in the UK only give university's the student loan cash once a student has progressed through certain stages of their course, for example) and committed expenses would still need to be paid, at least in part. So by cancelling it part way through they are likely to be left with a bigger deficit now than they would if they let it run its course, to illustrate:
Let it run it's course:
income - expenditure = deficit1
Cancel it now:
income - expenditure - refunds = deficit2
deficit2 > deficit1
And this is not to mention the reputational risk in cancelling a course with students already on it.
To answer your question, "What should I do?" I'd find out exactly why the course is for the chop midway through (there might be a very good reason why!) and then argue:
- that its financially more sensible to run with it at a loss rather than loose income to refunds (assuming this is true);
- that the risk to department/institution reputation is real (again, assuming that it is)
- for the ethics of disrupting students' learning partway through and potentially putting them behind in their educational pursuits by another academic year (this one is the key message!);
- for the academic/strategic value in running the course (is it an investment, does it make the college look good etc.);
- to outline strategies for improving recruitment network (collaboration with other programmes, better marketing, tweak the content), and
- if you deem it appropriate, to outline your personal inconvenience as a result of the cancellation (I'd imagine they want to keep good staff - as you hinted that you are - happy).
Voices from students, and their representatives, might be persuasive here as well.
Another reason I would be reluctant to cancel a course midway through is that the tutor would be under contract - so I'd still have to pay them. So, take a look at your contract and see what happens in the event of cancellation partway through.