Jaddie has still not told me how my screwdrivers get magnetised. And no, they dont come from the store like that.
I actually did, in another post, but again here's how it happens as I understand it.
Ferrous material has a natural magnetic state to which it will return if left uninfluenced by external fields. Sometimes that natural state is polarized, sometimes less so, and sometimes it is neutral to the point where it can't reliably be measured. If a material has a natural magnetic state of polarization, we call that a permanent magnet. How readily a material will accept a new polarization is a function of it's coercivity. How much it retains polarization is a function of its retentivity. Some materials have an ability to return to their natural polarization fairly quickly, even after their fields have been temporarily neutralized by degaussing. This can be seen in some (older) tape machine parts, where there's no magnetizing field present, yet the parts "accumulate" their own field. So one possibility is that the screwdriver's natural state is polarized, and it is to that state it will slowly return even after an attempt to demagnetize. I found many materials would do this when I had access to the Gaussmeter with hall effect probe.
If you're certain your screwdriver was not initially magnetized, one possibility is that it has very low coercivity, and can be easily magnetized by external fields. There is a pretty large .5 gauss field just about everywhere on earth. And much stronger fields around other metal parts. It could have taken on a polarization from an external field. Even in the steel office building where I did my testing, I found strong DC fields in various placed. AC fields were, of course, everywhere. One thing to know about AC fields is, we can't always assume they are capable of demagnetizing, as distortion of the magnetic waveform in one polarity or the other effectively produces a DC component which can obviously magnetize something. Distortion of the magnetic waveform is caused by various means, some of them also being a distorted electrical waveform, but that's one way to get a polarizing field out of an otherwise depolarizing system. But in short, there could have been an external magnetizing field present near the screwdriver, and it's material was easily magnetized.
Anyway, it pretty much has to be one or the other.