Do you know if you're dropping GRE packets or packets tunneled withing the GRE tunnel? With any sort of tunnel, it's not uncommon to run into MTU problems with just about any kind of tunneling. MTU problems can be hard to diagnose because smaller packets (like default pings) pass through the tunnel just fine. You'll only see problems with larger packets and generally only if the application or system is setting the DF (Don't Fragment) bit. Which unfortunately is pretty common.
You can test end-to-end for what's the smallest MTU across the network path by using pings with a large packet size and the DF bit set.
On Windows you can set the DF bit with the -f option and set the packet size with the -l option like this:
ping -f -l 1450
On Linux, you set the DF bit with the "-M do" option and set the packet size with the -s option, like this:
ping -M do -s 1450
You didn't say what you're using for the GRE endpoints.. If they are Cisco routers, this link is pretty good. If not, search google for GRE MTU issues and you'll find a ton of information.