This might be caused by traffic following the wrong route.If that is the case, here's an explanation and a fix.
If the VPN is interrupted shortly the FGT will send out the traffic intended for the private LAN on the other side of the VPN to the WAN port, following the default route. Once this session is established it is cached in the routing cache. When the VPN comes up again, there is already a session for this traffic and so packets are sent to Nirvana.
There is a quick fix for this: if you create blackhole routes for all private networks in use (192.168, 10.x.x.x etc.) with high distance values, they will be used instead of the default route if the VPN is down. The difference is that no sessions will be established to blackhole routes, thus no route cache entries. As soon as the VPN comes up again traffic is routed through the tunnel.
To faciliate this, I've written a batch command script which can be loaded onto the FGT. BH routes are not in use normally so this can be done even as a precaution. I don't think the script is FortiOS version dependent - you'll see.
You can download it in this forum post. Scroll down to my post near the end.