Oh, don't get me wrong ... I'm not trying to fix an engineering problem in software (although I'm often told to!). I've already located more robust pots. Also, the issue was that we stringed PWM cables together; and our robot's omni-wheel design was "knobbed" causing some pretty serious shaking; this all combined to let the cables come undone, even though they were wire tied, and the connectors taped for insulation. Next year, though, my team knows to just use plain old wire and only attach to the PWM connector at the very end of travel. This should allay most of the problem (though for 3 regionals we didn't have much of a problem at all).
The software detection is just an added step in the process, an extra redundancy (speaking of redundant ...). The issue isn't to come up with a kludge, but to detect failure in a specific system, and let that system revert to manual control individually, instead of relying on a general sensor override switch (aslo, in auto mode it is useful to know if the sensor isn't working, to go to a plan b, or at least to sit still so that the robot doesn't ram into the wall with pieces incorrectly deployed, causing us to get DQ'd, which did happen).
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but I think if you solved the reliability problems, the root cause of your failures, we would not be having this discussion at all - the best solution would be more robust pots attached in a manner that wont destroy them (couplers that can flex a bit maybe?)
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Oh, I agree with you that the reliability is the root cause and needs to be addressed first. (But as a programmer I can't sit idly by and rely on engineers, of all people, to fix the problem!

) Incidentally, one of the pots was attached to a spring type device that gave way and flexed as needed ... but the force became too great apparently.
I did think of adding limit switches, where the pots are used for detecting the end points of travel, to act as redundancies ... though, as you mention, I'd need a third sensor to know which one has failed. I don't know, perhaps if I fix the robustness problem all this won't be necessary at all -- did anyone else using pots experience any problems about failure? The issue that bugs me is two separate pwm cables went bad, which were kept safely away ... and that doesn't have to do with the strength of the pot's mounting or the pot itself.