What happened to the multi-colored Paradigm daleks? In terms of production and story. It's as if the BBC forgot about them.
Out of Universe answer
The New Paradigm Daleks were dumped after a backlash from fans who thought they were stupid and a blatant attempt to merchandise to small children. They were referred to on multiple occasions in media as being reminiscent of the Power Rangers, TellyTubbies or M&M's
Showrunner Steve Moffat admitted that they were a big mistake and that they would be relegated to the background of episodes as a little seen 'officer-class'
He was also asked about them more recently in a Q&A for Doctor Who Magazine. Suffice to say, his answer wasn't exactly filled with enthusiasm for the NP Daleks.
And in an interview with Who writer Nicholas Pegg, it was stated unequivocally that the major reason to abandon them was the poor fan reaction.
In Universe explanation.
As you can see from this grainy out-of-focus footage smuggled out of the 2011 Doctor Who Experience, there appears to have been a civil war between the New Paradigm (NP) Dalek and the old Prevailing (P) Daleks, proving that P≠NP.
That being said, there do appear to be some remaining NP Daleks, as evidenced by this image from 'Asylum of the Daleks'.
Out of universe
The multi-coloured Paradigm Daleks were unpopular among fans, and eventually Moffat decided to more or less phase them out, keeping them only as a rarely-seen "officer class".
Further discussion of the out-of-universe reasons for their disappearance can be found in this article.
There's no canonical answer in the TV show for what happened to the Paradigm Daleks, but a possible answer is provided by the Doctor Who Experience in Cardiff, which is perhaps semi-canonical since its storyline was written by Steven Moffat. In the story told there, the bronze Daleks exterminate the Paradigm Daleks because they don't consider them to be 'pure' enough (à la Dalek Sec in Evolution of the Daleks):
Dalek civil wars happened a couple of times in Old Who, so it's possible that a third occurred and led to the extermination of the Paradigm Daleks, following a brief period of Dalek cooperation in Asylum of the Daleks.
Further discussion of the in-universe reasons for their disappearance can be found in this article.