So users are local, you don't have a Security Server / Access Point / UAG in your implementation? What is the model of your HP thin client?

Are you connecting using Blast / PCoIP or RDP ? What version of the horizon agent is installed on your instant clones?

Are the thin clients in he same vlan with your connection server and the VMs? Is there a load balancer along the path?

Can you take a wireshark trace of your VDI session and examine the errors around the disconnect time? Wondering if the disconnects are related to the network configuration and not Horizon agent / client ?