We repaired press fit connectors at my previous job. As already stated, you need to have the proper design and construction of the PTH to begin. 

For our application (automotive) we pressed the entire connector out of the PWB. This requires some 'design for repair' such that the PWB can be properly supported with tooling during the removal process without damaging nearbly components via excess strain. The removal speed was very slow (12mm/min) to prevent damage to the PTH. We had a rule that no repair could be attempted on assemblies returned from the field due to the 'cold welding' that occurs with aging. Carefully inpect the PTH's for damage to the barrels. We allowed only one repair attempt per connector.

Regards,