QGraphicsScene::drawBackground lines thinner than coord units are not drawn

[Asquator]

I use the drawBackground method to draw a grid of straight lines.
I have a maximum availabe sceneRect size and wheelEvent in the view connected to a slot in the scene to dynamically change the grid scale, it looks like this:

The code that does the adjustments and calculates the lines' positions:

void PlotScene::drawGrid(QPainter *painter, const QRectF &rect){

    QPen pen = QPen(Qt::black);
    pen.setCosmetic(true);

    double gap = 1 / gridScale, level, extraRender;
    double top = rect.top(), bottom = rect.bottom(), left = rect.left(), right = rect.right();

    //horizontal
    painter->setPen(pen);
    extraRender = (right - left) * EXTRA_RENDER;

    //iterate from top to bottom and draw lines
    for (level = gap * round(top / gap) - gap; level < bottom + gap; level += gap) {
        painter->drawLine(left - extraRender, level,
                        right + extraRender, level);
    }

    //vertical
    painter->setPen(pen);
    extraRender = (bottom - top) * EXTRA_RENDER;

    //iterate from left to right and draw lines
    for (level = gap * round(left / gap) - gap; level <= right + gap; level += gap) {
        painter->drawLine(level, top - extraRender,
                        level, bottom + extraRender);
    }
}

The loops just calculate the grid's intersection with the visible rectangle and draw the lines.

The probem is that when I zoom greatly into the scene (in terms of single coordinates), the lines are not drawn at all:

So, when line coordinates are small double values (even 0.9 counts), the lines are not seen at all (even if I specify greater pen width).
That is, I can draw a line (-5,-5,5,5), but can't draw a line (-0.9, -0.9, 0.9, 0.9). On zooming out it works perfectly (until I totally zoom out of the scene).
What is the cause of this behavior and how can I fix it to be able to zoom more into the scene with a visible grid?

I tried to use setCosmetic and setWidthF methods of QPen, didn't help