The problem comes, in my mind, from the pid_file which is not found I think. This file must be external to the Capistrano versionning.
As describe on the documentation, you should have something like that in your thinking_sphinx.yml
:
production:
mysql41: 9312
enable_star: true
min_prefix_len: 3
utf8: true
pid_file: /my_project/sphinx/production.searchd.pid
indices_location: /my_project/pinchix/shared/sphinx
If you don't, as Capistrano is creating versioning folders, Thinking Sphinx won't be able to find pids on the the deployment folder (it's searching on the current one by default) an then will block because it can't start a new one if another one is already started (port not free).