After playing around a bit more with this patch, I discovered that OCSPStapling cannot get the issuer certificate if you use only the SSLCertificateFile directive. It works if you specify SSLCertificateChainFile, though.
Error only using SSLCertificateFile: 2014-02-04 19:07:13 [ssl|error] AH02217: ssl_stapling_init_cert: Can't retrieve issuer certificate! 2014-02-04 19:07:13 [ssl|error] AH02567: Unable to configure certificate foo.bar:443:0 for stapling