When will the certificate be download with Load balancer?

hi, experts
I have to confirm when will Certificates be download when EBS use load balancer.

May I asking the situation like below:

1. access load balancer, and the load balancer direct the access to AP1 server. (the certificate will be download)
2. for some network reason, the session got kicked off
3. then, access load balancer again, the load balancer will direct the access to other server(like AP2), does the certificate will be download again?

I did a test below:
1. access a server, during the java console, could confirm the certificate has been downloaded.
2. close the browser
3. access same server again, could confirm the certificate been download again.