Hi Chris,
Thank you for really prompt reactivity. Following your comment, I've updated all assets to Take 94 (initial install was performed with R81.10sp T338 and followed by updating with T81), also I'm sure T81 was very fine. Portfast was already set up on the network side, but I've checked again my configuration to make sure everything was ok. It appears that the uplinks used for the management bond of the security group were incorrectly set up. In fact both uplinks were not part of a port-channel on the network side, which messed up with the arp tables when the failovers occured. It has also shown me that the trafic I was monitoring was wrongly routed through the management bond (but that's an other problem).
Right now the failover is working fine, as I'm experiencing 1 to none ping loss during the process and the remediation.
Anyway, your guidance helped me fix the issue by leading me to the right troubleshooting steps to take, so thank you very much.
Have a nice day !
Lucas