GRE tunnel flaps every minute after OSPF replaced static routes

R1 (HQ) and R2 (branch) are joined by a GRE over IPsec tunnel (tunnel protection) that ran with static routes for years. Yesterday an engineer replaced the static routes with OSPF and, "to keep it simple", used network 0.0.0.0 255.255.255.255 area 0 on both routers. Since then the tunnel goes down and up roughly once a minute and branch users see constant drops. Each router reaches the internet with a static default route to its ISP.