Electronic – Op amp follower not actually following in LTspice simulation

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:

Here is the real behavior of almost the same circuit, installed in a real device.

The differences are that the driving source impedance is unknown (V1 is ideal in the simulation), and the load impedance corresponding to R3 in the diagram is unknown.

The behavior is nowhere near the rosy picture painted by the simulation. (On the other hand it is good enough that the everything works in the DUT).

The horizontal divisions on the graticule represent 500 nS intervals. The upper trace is the transistor's collector: one division is 5V. The bottom trace is from the base: one division is 2V. As can be seen, the rise time is quite slow, taking over 500 nS to rise to more than 90%. What might be considered a solid high logic level is probably not established for some 250 to 300 nS.