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Daniel,
The idea of the diode (germanium, then) is to stop current flowing from the 5V supply to the 3V (or so) battery, while there is a 5V supply, but to allow current (not voltage) to flow from the battery to the static RAM chips, when there is no 5V supply.
In an idealised view of how the circuit works, it behaves like an automatic switch.
However, no component behaves quite that perfectly. There will always be some reverse or leakage current, from the 5V supply to the battery, and there will always be a finite amount of resistance when it's conducting (forward biased) to power the RAM chips from the battery.
With a healthy diode, that reverse leakage current will be small enough not to matter - hence batteries which are not rechargeable being able to last for years.
One of the ways a diode fails is that the leakage current goes up dramatically. It might not happen all at once though. The two distinct layers of semiconductor start to break down, polluting each other, so the diode behaves less and less like a diode, and more like a resistor.
Another way a diode fails is simply that a gap forms between the two layers, typically due to a zap of high current, for a moment. In that case, the diode stops conducting, and becomes open circuit.
However, it's possible that a gap starts to form, with age, but not all the way across, so the two different pieces of semiconductor don't completely separate - maybe forming little pits or cavities. In that case, the forward resistance of the diode would start to increase - it would still pass current, when it was forward biased (anode voltage exceeds cathode voltage by a sufficient amount), but it wouldn't pass as much.
- Andy