What version of FortiClient and FortiGate Firmware? Have you checked the basics, I had an instance where DNS was stale and when I tried to reconnect DNS would still try to talk to the DNS servers from the VPN. For it going down though you can probably turn on logging within the forticlient by going to File > Settings and changing the log level to Debug. Recreate the situation and review the log file, It might point you in the right direction.
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