It is important to note that simply curing the error is not enough to make the SRS light go out.

SRS is a Safety of Flight item, it does not poll for system integrity and then shut the light off if the polling goes properly. It polls for the system components to 1.) be in place, and 2.) be operational. If either of these conditions fails, the SRS light comes on. The light will not go off until it is expressly reset by way of the diagnostic tools that are available. The light will never clear itself.

By way of comparison, you can have the Check Engine (SERVICE ENGINE SOON) Light come on, then replace the component that cause the event to be recorded, and the light will eventually turn itself off if the ECU is convinced that the issue is resolved. The ECU polls the vehicle systems it is interested in, and if a fault goes away then the light will clear itself -- turn off. The code that made the light turn on will revert from active to pending, and the light will go off. The SRS does not have the ability to do this, the SRS light must be expressly turned off through the diagnostic packages available for such things.