Last night as I was doing the security updates, I found a ward computer that was still running MLS 3.1.2. This was a older GX270, but the other GX270 we had in the stake hasn't had this problem. A check of the Windows Event Log showed it was last rebooted on Jan 3rd.

I didn't check the MLS log, but since I found MLS was already running, it wouldn't surprise me but MLS hadn't been restarted in some time as well.
When I rebooted the computer, MLS came up as 3.1.4. Since this is a dial-up machine with no other network access, 3.1.4 must have been previously download and just needed the reboot or restart to complete the job.
Something to check if anyone else finds a computer that's not updating MLS as expected.
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