Electronic – LTSpice noise simulation with custom noise voltage source

The solver is essentially solving a system of differential equations, and there are various algorithms for doing this, some which work better that others depending on the conditions ("stiffness" of the equation - if you know e.g. Matlab/Scilab/Octave see the various ODE solvers there for different conditions)

Depending on the circuit, the solver may have a hard time coverging, and as the Photon says shortens the time scale until it basically just slows down and stops (sometimes if you leave it long enough it will complete the "difficult" part, but often not).
This often happens when ideal capacitive/inductive elements are present, so it's always a good idea to select a series resistance for an inductor (actually defaults to 1m) and also an ESR for a capacitor. Right click on the component to set these and other values (as you probably know)

One other thing is your voltage source appears to be floating from circuit ground - add a high value resistor across the transformer (e.g. 100Meg) Without a DC path it makes it hard for SPICE to determine the nodes voltage.

The last thing I notice about your circuit is you have not selected a "real" diode - this may cause issues also. Right click and select a diode from the list available, I imagine this combined with setting some reasonable value ESR for the cap (and maybe a little more for the inductors) will make it work for either solver.

The circuit below works fine with either solver (cap has 1m ESR):

Simulation:

The most likely culprit I see is the switch who doesn't use negative histeresys, as recommended by the manual. Positive and/or no histeresys makes it switch abruptly between the on/off resistances, while a negative histeresys will allow a smooth transition, thus allowing the solver pass the hops with elegance and dignity.

For the ideal diode you could try adding epsilon=100m revepsilon=50m, they set the quadratic region of the I-V curve's "knee". Also, the dynamic resistances you chose for the diode are quite far one from another (in orders of magnitude), which could pose problems. I think it's more than safe to choose Ron=1m Roff=1Meg.