I tentatively believe that this might be fixed for me in B361. The covers stay after going offline, but there still seems to be a minor issue with the image in the album view showing as low-res although the hi-res must be available because it is used when I switch to the Now Playing screen. But this seems to fix itself over time maybe.
It has worked for 13 hours now after starting my test. I have to wait longer to be sure, but so far so good. Details in the post linked below.