Increasingly complex demonstrations of integrated circuit elements based on semiconducting single-walled carbon nanotubes (SWCNTs) mark the maturation of this technology for use in next-generation electronics. In particular, organic materials have recently been leveraged as dopant and encapsulation layers to enable stable SWCNT-based rail-to-rail, low-power complementary metal-oxide-semiconductor (CMOS) logic circuits. To explore the limits of this technology in extreme environments, here we study total ionizing dose (TID) effects in enhancement-mode SWCNT-CMOS inverters that employ organic doping and encapsulation layers. Details of the evolution of the device transport properties are revealed by in situ and in operando measurements, identifying n-type transistors as the more TID-sensitive component of the CMOS system with over an order of magnitude larger degradation of the static power dissipation. To further improve device stability, radiation-hardening approaches are explored, resulting in the observation that SWNCT-CMOS circuits are TID-hard under dynamic bias operation. Overall, this work reveals conditions under which SWCNTs can be employed for radiation-hard integrated circuits, thus presenting significant potential for next-generation satellite and space applications.