Not all street labels are shown when using osm2pgsql

I've used OSMBright as starting point to style my own map. There is just one little thing that goes wrong: in some area's (such as big city's) some streetlabels are not shown. When I look for the same streets on openstreetmap.org, they have shown. Is this a known issue?

Start by reproducing the missing street labels with OSMBright and osm2pgsql in a large-city area, then compare the rendered map with openstreetmap.org. Trace the label-rendering behavior and determine the cause of the omitted streets; done means the issue is explained and the affected labels render consistently.

Written by the indexing model from the issue text.