GRE Tunnel Problem

I have got two GRE tunnels from NOC to two remote sites and since I set these tunnels up, I got problem with one of the management softwares. It happens that it stops responding and generates "Time Out" messages when it is left idle for about 10 minutes and after 2 or 3 unsuccessful tries it comes back to life. All other connections (RDP, FTP, SSH) through these tunnels function smoothly at any given time but our NGN department engineers are getting annoyed once a customer calls, since they need to send their commands a couple of times until their software responds!
One GRE tunnel is setup between two Huawei Eudemon firewalls and another between a Huawei Access Router and an Eudemon firewall.
My studies show that this behaviour is due to over sized packets as a result of added tunneling headers.
I will be posting more on this issue once any progress made.