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Assume this is an IPSec VPN? If so all three tunnels will terminate on your network right?
Have you checked your VPN Concentrator/Firewall to make sure its interfaces are not dropping packets or misconfigured with speed/duplex. Check the cpu load/memory on the VPN Concentrator/Firewall.
Also check the bandwidth load inbound and outbound on your internet interface at the head office.
If the problem is affecting all remote sites then it's likely to be some sort of loading/performance issue on the main hub site.
The above assumes the topology is the remote sites are spokes and you are the hub with all routing between sites going via yourself.