Is there a stigma in computer science toward too many postdoc positions? I am wondering if there is a stigma attached to holding too many soft-money positions when looking for a tenure-track position in the area of computer science.

In computer science, postdoc positions were uncommon, but after the Dot-com bust and a general trend toward not hiring tenure-track faculty in the early 2000s, there are now many more postdoc positions in that discipline.

Do people who hold too many postdocs (or too long of a postdoc) get disadvantaged? Do they acquire a stigma of "This person can't hold a tenure-track job" or "This person bounces around too much" or "This person can't do independent research and relies too much on soft money"?

I know of a handful of faculty members who have been hired after multiple postdocs and visiting faculty positions so it seems that it isn't a permanent roadblock, but it could be a path I might not want to go down just in case it is.
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.