I don’t know how closely @manton monitors the feature request thread, but the Remember Posting Display Options one currently has 13 hearts. No, make that 14, I just liked it, too. 
As a workaround, if your browser supports custom stylesheets (CSS) for websites, this snippet should force the categories to always display in the web version of Micro.blog:
#posting_categories {
display: block !important;
}