Is there a stigma in computer science toward too many postdoc positions?
There are multiple simultaneous trends which are working against one another:


The number of PhD recipients is growing at a much faster rate than the number of available tenure-track positions.
More and more locations have been instituting term limits on the length of postdoctoral positions.
Hiring committees are not as receptive to applicants who have done too many postdoctoral positions.


This leads to a lot of challenges for many academic aspirants. Personally, my impression is that the dangers are as follows:


Remaining in any single postdoctoral position for more than about three years. 
Accepting more than two postdoctoral assignments.


Once either of those thresholds have been crossed, I think it starts to hurt an applicant later in their career. The exception to this might be "research professorships" and "staff scientist" positions that are seen to be more permanent than a postdoctoral position. Even in these positions, however, there is always the challenge that it can be difficult to transition to a different position afterwards.