The Interuniversity Consortium for Political and Social Research (ICPSR) maintains a persistent URL for each DOI. Example: http://dx.doi.org/10.3886/ICPSR06849. However, the link often points to some pay-walled article, even when it is freely accessible somewhere else. Is there any alternative service that maintains a persistent URL for each DOI, which points to a open access article whenever possible?
I'm not completely sure what you mean by "maintains a persistent URL for each DOI" - the point of a DOI is that it is the persistent identifier and the underlying resource can be shifted around as needed.
But answering the question...
Why, yes, there is -
This takes the DOI, looks for an OA version (loosely defined), redirects to that if found, and falls back on the original DOI target URL if nothing is available.
Two examples from a randomly chosen issue of Nature last year:
doi:10.1038/nature14178 > http://doai.io/10.1038/nature14178 - no OA version so falls back on Nature, the original DOI target
doi:10.1038/nature14260 > http://doai.io/10.1038/nature14260 - OA version available on PMC, so directs the reader there
A new open access DOI resolver was launched this week: http://oadoi.org/