It might help if you linked to the shop that you have mapped, to check if its tagged correctly etc - use the permalink.

Firstly, the online maps (Mapnik and Osmarender), can take a while to update, so its possible that they haven’t rerendered yet to show your changes.

Second, Mapnik and Osmarender do not show every type of amenity / shop / feature. If they did, the maps would be rather cluttered. From a quick check near me, it seems shop=hardware is not rendered on Mapnik or Osmarender.
Though its still worth mapping them, even if they don’t show up on these maps. There are other OSM based maps that do show them, eg OpenStreetBrowser or various Garmin maps.
And if you think it would be useful for Mapnik or Osmarender to render them, you can post a request on Trac.