From e.g. the Severnwaste recycling company (UK):
Plastic items are sorted by optical scanners which use the reflection of light to identify the types of plastics. Black plastic doesn’t reflect light, so can not be seen and sorted by the scanners and could end up contaminating other materials such as glass bottles. Microwave food trays which are normally black are also made of a special type of plastic which can not be easily recycled.
But in a forum post on TheRubbishdiet.com Joseph Kennedy from the PlasticExpert blog writes:
... in July (2014), Sainsbury’s and M&S began working together to alter the properties of the polymer to make it known to infra-red sorting technologies. So within a year we can hopefully expect to see this kind of plastic recyclable. This isn’t to say your council can’t recycle it.
They can, they just choose not to. The councils earn rebates on the materials they sell, which in turn helps pay for the council workers etc. Black plastic is the least valuable (that’s why your bin bags are black), and the reason is simple.
You can dye clear plastic black, but you can’t dye black plastic clear.
Black plastic is very low value, so your black food trays, bin bags, pvc guttering pipes etc, most often wont get recycled because they have little value on the other end of the market. It’s a money driven industry, like everything else.
The way in which the plastic is colored black makes a difference. From Recyclability of black plastic packaging at Wrap.org:
The majority of black plastic packaging is coloured using carbon black pigments which do not enable the pack to be sorted by the optical sorting systems being used widely in plastics recycling. As a result, black plastic packaging commonly ends up as residue and is disposed of in landfill or recycled into lower value materials where polymer sorting is not required.
WRAP has worked in partnership with key players in the retail supply chain to improve the recyclability of black plastics and prevent these materials from going to landfill.
This work was carried out in three phases and based on the results of this work, it is recommended that detectable black colourants be used as a viable option to carbon black pigments in the manufacture of black packaging such as amorphous polyethylene terephthalate (APET), crystallised polyethylene terephthalate (CPET), polyethylene (PE) and polypropylene (PP) packaging.
By selecting a detectable black colourant that enables the polymer to be detected by optical sorting systems the packaging supply chain can enable black plastic packaging to be recycled into a high quality, high value material which can substitute for virgin plastic in the manufacture of new items, and benefit the environment as well as the financial viability of mixed plastics recycling.
That last page has more detailed (technical) information.