You will notice that with regulators as you feed higher voltage, they have to dissipate this somewhere, usually a meaty heatsink will cure the cause.
My board with the 97J60 runs from a 19V Laptop PSU, 3.5A, it is feeding the actual HTPC as well as the control board, but I use a 12V 1A LDO, 5V 1A LDO and a 3.3V 300mA LDO (from Microchip) respectively, so I have the 12V running the 5V and the 5V running the 3.3V, works extremely well!
And, although they are heatsinked, the original bench version of the board was running a 12V 1A DC wall supply into the 5V reg, the the 5V into the MCHP 3.3V with NO heatsinks and it ran a bit toasty, but not anywhere near to thermal shutdown levels!
All regs were 1A LDO type apart from the 3.3V which was 300mA
I have noticed on the PICDEM2.NET board the 3.3V reg runs quite hot on there, but never blips at all.
As for capacitors, just oodle decoupling caps everywhere, especially on regs, I have never had an issue with cheap caps on a LDO or standard regulator before.
Wilksey