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E.g. if a given test were to generate a false positive, you would expect that it wouldn't generate a false positive the next time if run on the same article, especially if the machine correctly doesn't alert on other innocuous articles.Well yes, I would. Some false positives can be transient, others are not. If I just came from the shooting range I would not be surprised if I got a non-transient false-positive. Now that is an obvious case and I would immediately tell them that I had been to the shooting range, likely resolving the issue, but it is just a simple example of a false positive that is not transient.
How common is a non-transient false-positive where the victim doesn't immediately have a good idea what the cause is? Well, there are several reports from HN users in this thread that describe situations in which it could allegedly occur. One cites hand lotion as a potential cause of non-transient false-positives; luckily for his wife the agents volunteered that hypothesis so she wasn't left guessing. The author of the article supposes that an over-the-counter chemical was the cause of his non-transient false positive; it's not like he was a lab tech working with synthesized stuff that nobody else ever comes into contact with.
Unless the machines are shit (a distinct possibility), I would expect transient false-positives to be relatively infrequent while non-transient false-positives would be reliably and regularly caused by a wide range of substances that share chemical properties with known explosives.
Most of these non-transient false positives are likely quickly resolved without much ado. His was not.
Edit:
Perhaps the real problem here is with the terminology. These machines are not really bomb detectors, or even explosive detectors. They are chemical detectors. Calling them bomb or explosive detectors is like calling a metal detector a "gun detector". Sure, finding those things may be why it is there, but that is not actually what it does.