After upgrading to the recommended firmware of ZD1200, version 10.2.1.0.183.
We encounter an issue with the GUI of ZD 1200, there's a time I can't browse it, but my connection is stable.
Could you confirm if ZD is showing any error when you try to access GUI?
Are you accessing it from remote or locally? Are you able to SSH into it at the time when GUI is not working?
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You need to provide more details, to get help. Also, clean your browser cache. It may contain older version files. Use PC on the same subnet as ZD, to exclude any routing issues in the wired network.
In case if GUI really becomes inaccessible periodically, you could upgrade to some newer version, or try reapply upgrade there could be issue with upgrade process).
If nothing helps, you always can ask for RMA, as ZD1200 has life-time warranty.
current software release for zone director is 10.5.0.0.150 - you referenced the 10.2.x software released in your post.
Have you tried to verify connectivity to the ZD1200 via ping (icmp) or use SSH to access the appliance (in case you are experiencing a browser http/https related issue?