For some reason, the underlying algorithms (could be Direct2D or it's ancestor) considers the ratio StrokeThickness / Geometry extent and decides the stroke is invisible at some point (1 vs 125000). It's also somewhat mentioned here in this other question: WPF DrawGeometry does not draw stroke.

But the stroke is a brush, so you can trick the system like this, using a custom brush, for example in this case:

// use pen size instead of StrokeThickness
var geo = new GeometryDrawing(null, new Pen(Brushes.Black, 2), 
              new RectangleGeometry(new Rect(0, 0, e.NewValue, 1))); // use desired width for the geometry
var brush = new DrawingBrush(geo);
brush.Stretch = Stretch.None; // use this brush size, don't stretch to stroke thickness
brush.Freeze();
MyPath.Stroke = brush;

// choose a big number (more than desired thickness * 125000) to fool WPF or its friends
MyPath.StrokeThickness = 1000;