nintendo being a bit careless with the method they use for standby.
under the ABXY buttons is a little magnet switch.(under the X button for a phat)
if this switch is "hit" by the force of another magnet it will tell the DS the lid is closed, putting it into standby.
a bit careless of them is that they used a magnet as switch.
that means (as is the case here) that if the bottom of the switch comes in contact with the back of the lid's magnet it will cause a standby even when the lid is open.
this system is used with all DS models, however it doesn't cause problems with a phat.
most likely because the magnet is better shielded by the casing in a phat.(perhaps they simply forgot to retest the system after both redesigns)
there's a good chance the new XL DSi won't have this problem either since it's bigger allowing for some more shielding.
btw: putting 2 DS(i)'s on top of each other is as harmless as keeping the lid of your DS closed when you're not using it.