Hi Heidi,
As we were saying, it could be just because the program is written to not allow any node to exist without a DC path to ground so that it wont ever be able to develop an infinite voltage, but you could try connecting a large resistor across the cap to find out.
It could also be that it does not like the starting condition of a zero voltage across the cap when there is zero current through it and it's driven by a sine source. This results in a response not of a pure sine wave, but as:
1-cos(t*w) times 1/(w*c).
So we end up with a DC offset across the cap with a sine source. Maybe it doesnt like that.
The wave 1-cos(t*w) times any constant is a wave that is always above zero, not a sine wave.
I dont think you can build a pure sine wave current source with just passive components, but with active components you could build something that resembles this very closely. For example, if you had a source with non zero offset and you connect a large capacitor in series with it the capacitor will remove most of the DC offset, except for the leakage of the cap.
Alternately, you could put a DC current source in parallel with the sinusoidal source and control the DC current source with feedback from measuring the DC offset, and that should keep it very low. The precision would then depend on the precision of the control circuit. Back in the 1980's when i worked in the industry we actually had to do something like this with a synthesized sine converter design, where the slightly non symmetrical PWM input to the transformer would cause a DC offset current and that would push the operating point of the transformer up along the BH curve of the core, and that would cause operation that was closer to saturation for some points in the drive wave which in turn would cause more audible noise (audible noise is more of a problem with high power converters and many people did not want to sit in the same room with some of them).
So you might do a few experiments to see what is really causing the problem with your simulation, but in the end if you can solve it without affecting the circuit too much then you should be happy. If a 10 meg resistor does not compete with any other time constant in the circuit then i think you will do well to add a resistor