It is possible for a bad chip to cause stability or tuning problems, however, it's far more likely that the external heating resistor is bad (or the transistor controlling it is), perhaps a bad opamp in the control voltage circuitry, or even just old electrolytic caps. The ssm2033 is a really robust chip.
I would make the assumption that it isn't the ssm2033, and try to disprove your assumption by eliminating other possibilities.
-Steve