Experimental evidence, sample size of 1: a single layer of ordinary aluminum foil completely enclosing the card prevents a "normal distance" (4" square) reader from reading my card.

Another thought: is it possible there's exposed circuitry on the card that the foil is shorting out ? You could try wrapping it with a plastic bag before enclosing it with foil.

Are you sure it's a 125 kHz device ? Maxwell has never failed me before.

No, I'm not sure, but it does physically match the cards and readers in the article.

With no foil, the badge is read at 3-4".

With a single slice of foil ~18"x12" held in front of the sensor, the badge is read at ~1" (a noticeable reduction in signal).

With the foil folded in half and the badge in the fold so that it forms a single layer on both sides of the card, it was effective (could not read the badge).

With the badge in an aluminumized mylar antistatic bag, there was no evidence of a signal reduction (read at full distance).

I would theorize that Maxwell hasn't failed us, but the signal is weak enough that the foil attenuated the signal sufficiently to disrupt reading. The RFID reader works by modulating the sensor tuned loop by detuning on/off, which is going to be a pretty weak signal.

The read range you're seeing also seems compatible with a low frequency device.

I'm quite perplexed. I don't think the foil could be attenuating the signal directly. It might be reflecting it/altering the field pattern so as to reduce the effective gain between the transmitter and receiver antennas.