Shimano STI's have nothing you can adjust and they aren't repairable.
One possible fix is to thoroughly wash the shift mechanism out with a solvent like kerosene or mineral spirits followed by liberal lubrication with a light oil such as Tri-Flow. This often washes out accumulated dirt and gets the mechanism working again.
BTW, how old are the shifters and how many miles? 7-speed RSX hasn't been current for many years.