When the filament cathode gets too cold, the electron cloud that surrounds it becomes small. This cloud protects the cathode from positive ions, which are much more massive than electrons. Tohose ions are accelerated towards the cathode by the plate-cathode voltage, and when they crash into the cathode they will damage the electron-emitting surface and even dislodge small pieces. That's how cathode poisoniing works, as I understand it.
In these little battery tubes, the cathode is designed to function over a wider range of voltages than usual. In the Quickie, the actual current is much lower than the design maximum, giving a bit more margin. And the plate voltage is quite low, so the ions won't build up so much speed. All this should make the 3S4 in the Quickie pretty tolerant of run-down batteries, compared to non-battery tubes.