The exact situation you are in is not completely clear to me, I thus give a two-part answer assuming two different scenarios.
Scenario 1. The exercises are given by somebody else (the instructor of the course), and you run only the excercices-session.
The middle ground between 'enforce the students to do it themselves' and 'the tutor repeat it for them' seems like a good solution to me. The students in such a course already should have attained a certain level of mathematical maturity and are likley also somehow good students. So, if they do not prepare the exercises try to solve them on-the-fly together instead of just presenting them to them. Ask a lot of small questions, or ask for ideas they had/have. Also, do not shy away from trying ideas they have of which you know they will not work. To see the failing of the idea can be very instructive and lead to finding a better one.
Scenario 2. You have full control.
Something that can work is to run it almost like a (students') seminar. Instead of excercises hand out to each student (or small groups) a couple of pages from a book (or paper) of closely related material and let them prepare and present this material in class. Some points in favor:
They might find this more interesting as it adds something new and is perhaps different in style from other courses.
It might better teach them skills (understanding new material and presenting it) they need at that point of their developpment than the classical excercices-setup.
They do not have to work each week a bit, but at some point a lot. This could be a better fit with their time-management at that point.
The approach in scenario 1 is not really limited to advanced students but I think it is more feasible than, and at least it tends to work better with small groups. So far I never found an occassion to try the thing I describe in scenario 2 myself but know some people that do this (they sometimes use the time-slot for excercises-seesion at the beginning of the term for addition courses to have some weeks towards the end for the student presentations).