I have some Fortigates that close a BGP session with an ISP equipment. I notice that at times some FGT need to clear the BGP session to reestablish connections with the prefixes.
NOTE: Both advertising and received routes remain intact, without changes.
it could be interesting to know the reason of the "closure". You can get the information from "get router info bgp neighbors xx.xx.xx.xx" where xx.xx.xx.xx is the IP address of the peer.
You can also get the status of the connection using 'get router info bgp summary'.
Could you pleases also provide the FortiOS version you are using.
If you can get a pcap, you might know more but refresh means somebody changed something from a route-policy. For OP, did you receive the refresh or did you send this? Maybe a hard reset was being deployed due to that "refresh"
I pretty sure you can see bgp sessions details and number of route-refresh.