Why do some editors/journals withhold response letters from reviewers? I recently reviewed a paper for which I recommended rejection. I wrote a comprehensive review with a list of items that needed fixing to motivate my decision. I spent some time (between a day and a day and a half, perhaps) carefully reading the manuscript, writing and motivation my review.

Today I was curious to see what happened to the paper but since the journal uses Manuscriptcentral, the information regarding what decision was taken does not appear on the online system. I googled the title and found out that the paper has indeed been accepted by the journal. Having a quick look, it is obvious from its present form that the authors did receive my review and made changes accordingly.

I would have expected to receive a response letter to my review, especially within the context of my negative recommendation. However, this did not happen. On the one hand, I understand (and fully respect) that it's up to the editor whether to follow a reviewer's recommendations or even fully discard their review. On the other hand, given that I spent some of my time producing the review, it would have been nice to at least be able to see the response of the authors (even if not requested to produce a second review). Precisely because the paper was eventually accepted, I would have liked to read the author's criticism/rebuttal of my own criticisms - I might have been wrong after all.

What is the reason behind some journals keeping reviewers "in the dark" regarding what happens to the paper? Would it be appropriate to ask the editor to have a look at the author's response letter?
You learnt that the  authors' response was essentially "we accept the reviewers comments and have revised the manuscript accordingly."  If such revisions were clear to the editor there's no need for further review or communication.  

Don't forget that while you may turn reviews round quickly (or you may not), there are plenty of reviewers who even for a second review  have a high chance of sitting on the paper for an unreasonably long time.  This (on top of workload) is a further incentive for the editor to minimise unnecessary links in the chain.