Same thing happened to me. I first ensured the cable stop was seated correctly in the shifter, then sprayed the heck out of the shifter body with solvent. When these failed I took it to the LBS where I bought the bike. They spent a day or two, the gave up. Luckily, I was 3 weeks short of the Shimano 105's 2 year warranty period. They stood by the product and replaced it.

Last resort, but this seems to be known and common failure mode of the STI shifters.