Changing a dimension always immediately resets to 0 I have an object that was originally imported as an .svg, but I converted it to a mesh. However, blender still will not allow me to give it a size for the third dimension. The file can be downloaded from here.
What is it about this object that prevents me from setting a non-zero value for its Y dimension (in the 'n' dialog)?
Dimensions work as a scale multiplier. As your mesh has a Y dimension of 0, you can multiply it by any number, the result will always be 0.
To get thickness you need to enter edit mode, select all and press E to extrude the faces.
Once the object has Y dimension different than 0 you will be able to vary it in the N panel.
Be aware that you have the snap option activated.