As I understand you have two networks, one public (failover) and private (real).
I have two theories:
[LIST]
[]firewall issues (public IP has more strict rules)
[]routing issues (connect to the server is going via one network and answers are going via another network)
[/LIST]
Firewall: It is needed to allow traffic:
[LIST]
[]from PMM client any port to PMM server 80 and 443 ports
[]from PMM server any port to PMM client port 42000 for linux:metrics
[]from PMM server any port to PMM client port 42002 for mysql:metrics
[]from PMM server any port to PMM client port 42003 for mongodb:metrics
[*]from PMM server any port to PMM client port 42004 for proxysql:metrics
[/LIST] Routing: How to add PMM client over public network