nRF9160 modem stuck in searching

The modem on the nrf9160DK (modem fw v1.1.0) appears to get stuck in searching mode. It doesn't happen all the time, and I was able to create it with the following AT commands:

(I want to see registration status changes)
(after some time (minutes?) reports AT+CEREG: 2, ...)
(then I see no more +CEREG status reports and give up)
(wait a few seconds)
AT+CFUN? reports +CFUN: 4, so it seems to have taken the command
AT+CEREG? reports +CEREG: 0,2,"XXXX","XXXXXXXX",9

This all works just fine with %XSYSTEMMODE=1,0,0,0. After the AT+CFUN=4 completes it will report +CEREG: 0,0,...

I kind of expect the connect to work with either mode, as I have good reception from both AT&T and Verizon, but I'm more concerned that the modem appears to get in an *almost* unrecoverable state. Changing systemmode to 1,0,0,0 followed by AT+CFUN=1 returns to normal behavior.

If it helps in troubleshooting, the AT+CFUN=4 takes ~3 seconds in mode 1,0,0,0 and less than 1 sec in mode 0,1,0,0

This link describes a similar issue: