Teleport-agent fails to failover tcp connections to applications

[xe-leon]

Expected behavior:
proxied tcp connections are failovered to new registered teleport-agents that publishes this tcp application

Current behavior:
Tcp connection fails after few iterations of new teleport-agents

Bug details:

• Teleport version
  Teleport v14.2.1 git:v14.2.1-0-ge6737fe go1.21.4
  Proxy version: 14.2.1

• Recreation steps:

1. Run teleport agent as kubernetes deployment with 2 replicas with same tcp application to load balance
2. Launch tsh proxy app and check for connectivity
3. Kill 1st pod of teleport agent
4. Check for connectivity (success)
5. Wait 5 minutes to let new pod of teleport agent to register in teleport cluster
6. Kill 2nd pod of teleport agent
7. Check for connectivity (success)
8. Repeat same process killing new replicas of teleport-agent
9. After some repeatings proxied tcp connection fails, restarting tsh proxy app doesn't help until I run tsh apps logout

#53350