There are issues using the PicoPSU-90 with the Intel D2500CC Mini-ITX motherboard. When the board is in the ON state the power supply operates correctly but when the board is in the OFF state the power supply repeatedly tries to power up the board and then powers it down again every second or two. Testing the motherboard with a normal desktop ATX power supply did not show the same symptoms and identified the problem as the PicoPSU. The PicoPSU supplier, mini-itx.com, were contacted and they suggested installing a 10kΩ resistor on the PicoPSU between +5VSB and PS_ON#. Carrying out this modification (see the pictures below) fixed the issue.
It looks like the PS_ON# signal is connected directly to the TPS3510 power supply supervisor chip and that the pull up to +5VSB recommended in the ATX power supply design guide is absent. The guide indicates that the motherboard should be able to bleed 200µA from PS_ON# without the power supply starting, but the chip will start the power supply at much lower currents than this. The addition of the 10kΩ pull up reduces the sensitivity of the PS_ON# input. The guide indicates that the pull up value should be somewhere between 3kΩ and 10kΩ.
Since my initial tests with a 10kΩ pull up I have changed the resistor value as I would still get the occasional attempt at powering up whilst the board was meant to be off. I am now using a 4.7kΩ pull up resistor. This seems to have resolved the issue and the board now stays off.