Do these cards fall under Reg E?

One can argue on both sides of this question. In general, there seems to be agreement that if the card is rechargeable it's subject to Reg. E.

The Fed floated some proposed Reg E amendments a number of years ago that addressed just this question. The proposal, although never withdrawn, appears to have died a quiet death. I get the impression the Fed didn't want to stunt any innovation in this area.

A literal reading of the definitions in Regulation E could lead one to believe that stored value cards are subject to the regulation if the balance is maintained at a host (off the card).

I agree with John. The impression I recall having was that they would fall under E, but if they did you had statement requirements, possible FDIC insurance issues, etc... and they didn't want to delay an innovative product.

The recent OCC publication on Payroll Cards says this:

Consumer Compliance Issues
The Federal Reserve Board has not ruled as to whether electronic deposit accounts are subject to disclosures under consumer protection regulations, including Regulation E (Electronic Fund Transfers). However, the banks that we surveyed stated that they provide the disclosures described in Regulation E to their payroll cardholders.

As I recall, the debate in the mid-90s focussed on whether the stored value could reasonably be called an account. Since Reg E only applies to consumer asset accounts, the stored-value device would need to exhibit some of the characteristics of an "account" to be covered.

And that is why, according to my rapidly graying gray matter, the Fed at the time suggested that only on-line accounting cards with balances over $100 would be fully covered.