Sounds like you may have several things going on.
For computers disappearing from the console…a computer failing to find a relay or send reports, does not remove it from the console. You may have automatic computer removal set in the BESAdmin Tool (check the Maintenance tab). There are options to delete computers that haven’t reported in a number of days; check that your value, if set, is not too short.
If your clients are set to Automatic Relay Select, ensure they can Ping your relays. The client determines the distance to relays via ICMP Ping messages. It sends a series of pings to all the relays, starting with a TTL of 1, then increasing it until a relay responds or it reaches the MaxTTL value. If your clients are selecting a relay too far away, the MaxTTL may be too high or the ICMP traffic maybe blocked. Check that your VPN rules allow both ICMP and your BigFix port (tcp/52311 by default).
The relays that it attempts can be tuned with the Affiliation SeekList of the client, and the Affiliation AdvertisementList of the Relay. If you are setting values for either of these, ensure you are setting values for both the clients and the relays; else you may find the clients not even attempting to use the relays you want. Common errors there are to base the values on IP Subnets or Active Directory Sites, which may not resolve as you expect when on VPN.
If the client can’t find a relay at all, it will fallback to the root server (again, by default) without trying the ping; just sending the BigFix TCP traffic and hoping for the best. At this point it’s in ‘Failover Relay’ mode, tunable with the
_BESClient_RelaySelect_FailoverRelayList client settings, or the FailoverRelay defined via the BESAdmin Tool.
You can turn on debug logging at the client and perform a Relay Select to see how the client is behaving. Or you can engage a support ticket and they can help you through the process.
All these settings and many more described at https://help.hcltechsw.com/bigfix/9.5/platform/Platform/Config/r_client_set.html#r_client_set__arhd