For Al foil thickness I'm seeing conflicting numbers from 0.2 to 1.1 mm. If my cheap digital micrometer hadn't died I'd measure some.
If my skin depth is right then the attentuation probably won't be complete, if yours is then it might nearly be. Of course that's only the case if the receiver and/or transmitter is completely wrapped. Although at low frequencies like that you could probably tolerate quite a large gap.
My cheap digital micrometer only has two digits of precision in mm mode. Measuring my cheap (not "heavy duty") aluminum foil is at the limits of its resolution, 0.01mm.
In that case I would predict that a single sheet would have little affect on an RFID device operating at 125kHz. Note however that RFID devices appear to span a very large frequency range :
http://www.rfid-handbook.de/rfid/frequencies.html
and the foil would certainly block the higher frequency devices.
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.
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.