...
At Gordon's suggestion, did a bunch of tests of check_router script (which should have fixed this problem by itself). It has a long time-out of 3--5minutes, but did work as expected with the LAN cable unplugged. We next want to run a test by unplugging the 3G modem, but ran out of power on our laptop. We'll do this test tomorrow on the spare in the base.
P.S. The next day, we did this test on the spare, which worked exactly as expected. Thus, this failure at wvally4 is still a mystery.