hi,
I'm not sure if I know of another option. I am guessing that you have already tried Gene ID converters. Like one on DAVID. Depending on your biological questn., if you think that those IDs are must to be annotated then I think you can try this -
For those missing, from the Cufflinks result file, you should have the genomic coordinates. You must know at least if its hg19 or earlier or latest ver. And then use those coordinates and a latest gene anno file (NCBI, Ensembl, whatever suits you) to find out whom those coordinates overlap to. I think that should solve your issue.
This should work with the UCSC table browser:
https://genome.ucsc.edu/cgi-bin/hgTables
Select assembly: hg19, track: Ensembl Genes, output format: selected fields from primary and related tables and then "get output". Under linked tables pick hg19.knownToEnsembl, hg19.knownToRefSeq and hg19.kgXref (using allow selection button at the bottom in-between). Then just check whatever columns you want (gene symbol, ensembl ID, RefSeq ID, etc.) and press "get output". This should create a tab-delimited file with the desired information.