This is actually a good link; I ventured to this thread (in particular always an interesting topic when Nick Gammon chips in) 
It is this comment that got my attention:
I do run all my Arduinos with the W5100. I noticed on the odd one that it could not reconnect to the network, because the W5100 board seems to be in an undefined state (after the reboot; or needs more time to to get itself sorted.
E.g. if I hit the reset button while power was already ON, the W5100 connected; but if I switched ON power, the W5100 may fail to connect. This problem was solved tby adding a delay(500); at the beginning of the setup() function.
Certainly something I will look at.
As for brown out; I cam currently imagining I could use another Arduino to measure the 5V input voltage of the 'flaky' one while in normal operation... and let it 'phone home' to log any under-voltage events.
Thank you all for giving this post a go. 