Duh!
Just realized that the node is sleeping while waiting for the message!
There are no debug messages while waiting, the node just sleeps.
What threw me off, was that the time and date are received OK, but that was at the beginning of the first loop, while the node was awake.
I'll try the request() function ASAP.
Thanks.

How about a version with the SDA & SCL pins also routed to the header?
Sensors like the Si7021 are using the I2C interface

OK, problem solved.
First of all, I stopped using SoftSerial, and I am now using the regular serial port.
I can't debug the node any more, but it is working.
And the drain dropped to 1.9 mA.
This is the US100 idle current, so that was also a problem.
So I chose to power the sensor from pins 3 & 4, as VCC and GND, since just using pin 3 and GND kept the drain to 1.9mA
I turn pin 3 to output high and pin4 to output low, wait 5 seconds to let the sensor stabilize, since it gave erratic readings with anything less, take the measurement, and turn pins 3 & 4 to inputs, so there is no drain.
Seems to work so far, after a whole day of taking readings every minute, I am down by 10mV. I intend to take readings every 2 hours in normal operation, so I figure the batteries will last for about a year.
I am writing this from my phone, so I cannot post the source if anyone is interested, but let me know...

@mfalkvidd sorry, I was talking about the US-100 distance sensor. Jumped the gun here.

@Nca78 So, the capacitor is on the other side of the board, it just doesn't show in the photos. No problem with the SMD components, they are large enough if you are a bit careful.
You are wasting precious time writing in the forums. Get back to work! :-)