If there are multiple EIGRP and OSPF neighborship flap over the GRE tunnel what could be the problem and how would solve it?

If in the logging you are getting the error message

%TUN-5-RECURDOWN: Tunnel0 temporarily disabled due to recursive routing

It means that GRE Router tunnel has found a recursive routing problem. The symptoms of this issue include the continous flapping of tunnel interface as well as EIGRP,OSPF & BGP neighbours when neighbours are over the GRE. To resolve this issue you need to configure the static route for the tunnel destination.