Hello Olu,
you have not provided enough information in order to be helped.
Generally speaking:
we don't see a direct relationship between GRE tunnels and virtual-templates
And it is normal to see a virtual-template down because it is a logical interface used for deriving virtual-access objects used with PPP or L2TPv2 for example.
I understand you would like to send different sets of routes to different neighbors.
EIGRP allows to use ip eigrp summary-address on a per interface basis.
So one way to achieve what you want is to use 3 point-to-point GRE tunnels and to build EIGRP neighborships over them rather then the common LAN segment (so you passive the physical interface under router eigrp process)
In this way you have the capability to:
use different sets of summary address per GRE tunnel interface
you can also use distribute-list out referring to each specific GRE tunnel under router eigrp process.
Hope to help
Giuseppe