Thanks Dries for your message.
From my experience with the NHS3100, SWD probe failure can happen even without Power Off or Deep Power Down mode. A RESETN pulse always make the SWD probe happy. Good enough to reliably program the NHS3100 with OpenOCD (more reliable than the LPCExpresso).
I use a hacked configuration for openOCD that ensure a pulse is send to RESETN before SWD probing. It only work with FTDI adapter. This example use ADBUS7 as RESETN signal:
ftdi_layout_init 0x0000 0x00fb
ftdi_layout_signal nSRST -ndata 0x0080
reset_config srst_only srst_nogate connect_assert_srst
The trick is to init the FTDI IO with RESETN low and to make OpenOCD think it must assert the SRTS by in fact pull the RESETN signal high. With this, OpenOCD manage the RESETN signal the wrong way, because the logical level is inverted. But since OpenOCD don't need the SRTS signal for normal operation, this have no bad consequences, at least to just program the flash.