I found that with the latest updates on the Plasma testing edition (5.16.1) that the Software Center doesn't open. I ran it from the terminal and discovered an issue with the icon theme.
(solus-sc:2015): Gtk-WARNING **: 13:48:10.060: Theme directory 32x32/apps48x48/apps of theme solus-sc has no size field
(solus-sc:2015): Gtk-WARNING **: 13:48:10.060: Theme file for hicolor has no name
(solus-sc:2015): Gtk-WARNING **: 13:48:10.060: Theme file for hicolor has no directories
(solus-sc:2015): Gtk-WARNING **: 13:48:10.060: Theme file for hicolor has no name
(solus-sc:2015): Gtk-WARNING **: 13:48:10.060: Theme file for hicolor has no directories
gtk-icon-theme-error-quark: Icon 'package-x-generic' not present in theme solus-sc (0)
(solus-sc:2015): Gtk-WARNING **: 13:48:10.090: Theme directory 32x32/apps48x48/apps of theme solus-sc has no size field
(solus-sc:2015): Gtk-WARNING **: 13:48:10.090: Theme file for hicolor has no name
(solus-sc:2015): Gtk-WARNING **: 13:48:10.090: Theme file for hicolor has no directories
(solus-sc:2015): Gtk-WARNING **: 13:48:10.090: Theme file for hicolor has no name
(solus-sc:2015): Gtk-WARNING **: 13:48:10.090: Theme file for hicolor has no directories
**
Gtk:ERROR:gtkiconhelper.c:494:ensure_surface_for_gicon: assertion failed (error == NULL): Icon 'image-missing' not present in theme solus-sc (gtk-icon-theme-error-quark, 0)
I was able to get it working by installing adwaita-icon-theme and setting it as the fallback in the Plasma GTK settings. Just thought I'd post this in case anyone else runs into this issue.