The problem is that adding blocks to your model (such as the XY Graph) causes the sorted order of all the blocks to change. Since there are no clear data dependencies in an algebraic system like this (which Simulink normally can use to provide a consistent sorted order), adding blocks can cause seemingly random changes. There is nothing special about the XY Block in particular, you will get the same issue if you add a display block to both the X and Y signals for example.
I believe the problem with changing the sorted order is that depending on which blocks are executing first, Simulink will automatically select an initial guess for that block's output. If that guess happens to be poor, the solution will diverge and you get no answer. If that guess is reasonable then it will converge on a solution.
When you want to force Simulink to solve an algebraic equation, a good approach is to use the Algebraic Constraint block. This allows you to explicitly specify an initial guess for one of the parameters and have a more consistent result. For example, here is a revision of your model using the Algebraic Constraint block with X as the algebraic state:
