Effect of Gaussian Blur on Different Frequency Components of an Image
Gaussian Blur is Spatially Invariant Linear Filter.
Hence it can be analyzed in the Frequency Domain which in fact shows its Low Pass properties.
Namely it attenuates High Frequency Energy.

In Image, Edges, which are abrupt change from one color to other, requires high frequencies in order to be local.
Gaussian Blur attenuates and smear it.
As written above since it is Spatially Invariant, it behaves the same on DC zone or Edge.

Now, there are families of "Edge Aware Filters" which are adaptive to the neighborhood they operate at:


Bilateral Filter.
Non Local Means Filter.
Median Filter.
Guided Filter.


All of those react to the properties of the pixels they operate at hence can not be defined in Linear Convolution (Spatially Invariant).