I hear this mythical date in 2140 when we find the last scrap.. but does it have to be.. if only we could keep halving.. for-EVER!
You'll be adding an ever smaller number of Bitcoins per block. There's no point increasing the total Bitcoin supply by - say - 0.00000000000001% per block. The limited supply is by design, and it's one of the things that makes Bitcoin better than fiat.
It would still take some time to exceed the 21 million cap, though. My understanding was that currently there will never be more than 20999999.9769 BTC in circulation (or technically 20999949.9769 BTC due to the unspendable genesis block). Adding more decimal places and dealing with sub-satoshi units would not create enough extra BTC to make up for the 2310000 satoshi shortfall for many years, if ever.
//EDIT: Unless my math is wrong, which I'm starting to think it is.
//DOUBLE_EDIT: Nope, seems okay:
20999999.97690000
+
(210000 blocks x .5 satoshi) 0.00105000
=
20999999.97795000
+
(210000 blocks x .25 satoshi) 0.00052500
=
20999999.97847500
+
(210000 blocks x .125 satoshi) 0.00026250
=
20999999.97873750
+
(210000 blocks x .0625 satoshi) .00013125
=
20999999.97886875
+
(210000 blocks x .03125 satoshi) .00006562
5 (nine decimal places)
=
20999999.97893437
5 (nine decimal places)
So yeah, that's another ~20 years without crossing 21 million BTC and I'm sure if I kept going, it's okay for some time, or possibly forever.