Hello!
I don't know exactly how EZVPN is working, but if you redistribute connected than you will have no problem with OSPF, not matter how stable is your link to VPN remote site. You will always have an interface into the direct connected subnet which is redistributed to OSPF, and OSPF will always see this (as log as the IP is there) and advertise the subnet.
The problem is that your packet from LAN, to a remote VPN site reach OSPF router which is forwarding the packets through it's directed connected interface. If the remote end is not reachable the packet is discarded on the interface.
If you would have OSPF process with your VPN remote end, and this is flapping a lot, that's another story. You can have bigger hello time interval and dead interval and this will make OSPF process reconverge not so often.
Hope this is clear!
Cheers,
Calin