Why does the red color channel lose the most details during jpeg compression
One issue is "chroma subsampling". The image data of a JPEG is not stored in packed RGB but YCbCr as 3 seperate planes. The Cr and Cb channels contain colour information and the Y channel is luminance. In JPEG it is common to use a lower resolution Cr/Cb channel, typically at half the resolution of the Y channel, this is know as 422 Chroma subsampling (another variant is 420 where only the horizontal resolution is halved).

What you can do is select 444 Chroma subsampling, if possible, which will mean no down-scaling of the Cr/Cb channels. 

In Gimp you can select the subsampling type in "advanced options" when exporting JPEG files. This is independent of the quality setting slider.

There is a great image from wikipedia which compares the various subsampling modes side-by-side with a visualisation of one of the chroma channels, you can see the red decal in the centre is most affected by downscaling as that channel has high contrast edges



Wikipedia article for Chroma Subsampling