It didn't occur until the next reboot, at which time the problem returned.
I think I understand why the testing script (auto_check_SMS_Visible.sh) kept/keeps SMS alive on my router: it toggles the modem ON/OFF when it first runs. Reformatted for legibility:
# off
gl_modem -B $BUS AT AT+CFUN=0
sleep 1
# back on
gl_modem -B $BUS AT AT+CFUN=1
For whatever reason on my X3000 a modem reset keeps Visible SMS running (or restores SMS after it has died). Having those AT commands in the test script accidentally made the problem disappear; a Heisenbug.
For testing I'm dorking around with a smaller script called from /etc/rc.local.
More info in this blog entry since there is a time limit on edits here.