OK, we re configured HAproxy and it now works, here is the new config file:
global
debug
defaults
mode http
timeout connect 5s
timeout queue 300s
timeout client 300s
timeout server 300s
frontend http-in
bind *:8080
default_backend xx
backend xx
cookie JSESSIONID prefix
server xx_SERVER1 10.0.110.44:8080 cookie JSESSIONID_SERVER_1 check maxconn 500
server xx_SERVER2 10.0.110.45:8080 cookie JSESSIONID_SERVER_2 check maxconn 500
option httpclose
option forwardfor
balance roundrobin
option redispatch
retries 15
listen admin
bind *:8081
stats enable
stats refresh 1s