"+CMTI" is the unsolicited result code to notify you that a new
SMS has arrived.  I assume that you are getting this code as
soon as an SMS is received.  If not, you may be able to read a
new mesage using a "AT+CMGR" command, for example before you
get the "+CMTI" notification, and this would indicate a bug in
the modem's firmware.

But from what you've said, I think that new SMSs are not being
delivered to your device when you move from a region without
coverage into a region with coverage.  I can think of at least
two reasons for this.

If the SMS is being sent from a device on different network (and
therefore using a completely different SMSC), your network
might not be notifying the originating network's SMSC when your
device has done a routine location update.

Alternatively, perhaps your own network doesn't know that your
modem is available.  This can happen if your modem leaves the
coverage area after registering, and then returns to coverage
sometime later.  In the meantime, the network may have tried to
deliver an SMS, failed, and marked your modem as absent.  But
your modem knows nothing of this, and will not transmit a
location update until its T3212 timer has expired in the normal
course of events.  Only then will the HLR mark your modem as
present and make another SMS delivery attempt.

Assuming you're writing your own software, I suggest trying the
following.  Monitor signal availability and registration status
with "AT+CREG".  When coverage disappears and then returns,
force an network interaction, with "AT+CLIP?" for example.

If "AT+CLIP?" doesn't work, try deregistering and reregistering.
Depending on the modem, "AT+CFUN=0" followed (after a pause) by
"AT+CFUN=1" would do this.

John