Narrowing this down a bit more... I can see that the DHCP client is in an error status, and 'searches' every ~ 14 seconds - which is what takes away the default route.
The thing that confuses me - it's getting a lease with a DNS server and creating the default route.
These are the logs from one poll of the DHCP - repeat this once every ~14 seconds.
09:43:58 dhcp,debug,state dhcp: dhcp-client on ether1 entering <selecting...> state
09:43:58 route,debug,calc dhcp: Begin calculation
09:43:58 route,debug,event dhcp: Removed route
09:43:58 route,debug,event dhcp: state=CANDIDATE
09:43:58 route,debug,event dhcp: dst-prefix=0.0.0.0/0
09:43:58 route,debug,event dhcp: attributes
09:43:58 route,debug,event dhcp: protocol=DYNAMIC
09:43:58 route,debug,event dhcp: distance=1
09:43:58 route,debug,event dhcp: scope=30
09:43:58 route,debug,event dhcp: target-scope=10
09:43:58 route,debug,event dhcp: next-hop= address=10.11.1.250
09:43:58 route,debug,event dhcp: vrf-iface (1)=ether1
09:43:58 route,debug,event dhcp: origin-type=DYNAMIC
09:43:58 route,debug,calc dhcp: Select route
09:43:58 route,debug,calc dhcp: dst-address=0.0.0.0/0
09:43:58 route,debug,calc dhcp: attributes
09:43:58 route,debug,calc dhcp: protocol=STATIC
09:43:58 route,debug,calc dhcp: distance=1
09:43:58 route,debug,calc dhcp: scope=30
09:43:58 route,debug,calc dhcp: target-scope=10
09:43:58 route,debug,calc dhcp: next-hop= address=10.11.1.250
09:43:58 route,debug,calc dhcp: comment=
09:43:58 route,debug,calc dhcp: origin-type=STATIC
09:43:58 route,debug,calc dhcp: End calculation
09:43:58 route,debug dhcp: Begin redistribution
09:43:58 route,debug dhcp: Skip update 0.0.0.0/0
09:43:58 route,debug dhcp: End redistribution
09:43:58 dhcp,debug,packet dhcp: dhcp-client on ether1 sending discover with id 524268713 to 255.255.255.255
09:43:58 dhcp,debug,packet dhcp: flags = broadcast
09:43:58 dhcp,debug,packet dhcp: ciaddr = 0.0.0.0
09:43:58 dhcp,debug,packet dhcp: chaddr = 74:4D:28:78:32:ED
09:43:58 dhcp,debug,packet dhcp: Msg-Type = discover
09:43:58 dhcp,debug,packet dhcp: Parameter-List = Subnet-Mask,Classless-Route,Router,Static-Route,Domain-Server,NTP-Server,CAPWAP-Server,Vendor-Specific
09:43:58 dhcp,debug,packet dhcp: Host-Name = "rb04"
09:43:58 dhcp,debug,packet dhcp: Client-Id = 01-74-4D-28-78-32-ED
09:43:58 dhcp,debug,packet dhcp: dhcp-client on ether1 received offer with id 524268713 from 10.11.1.250
09:43:58 dhcp,debug,packet dhcp: flags = broadcast
09:43:58 dhcp,debug,packet dhcp: ciaddr = 0.0.0.0
09:43:58 dhcp,debug,packet dhcp: yiaddr = 10.11.1.249
09:43:58 dhcp,debug,packet dhcp: siaddr = 10.11.1.250
09:43:58 dhcp,debug,packet dhcp: chaddr = 74:4D:28:78:32:ED
09:43:58 dhcp,debug,packet dhcp: Msg-Type = offer
09:43:58 dhcp,debug,packet dhcp: Server-Id = 10.11.1.250
09:43:58 dhcp,debug,packet dhcp: Address-Time = 86400
09:43:58 dhcp,debug,packet dhcp: Renewal-Time = 43200
09:43:58 dhcp,debug,packet dhcp: Rebinding-Time = 75600
09:43:58 dhcp,debug,packet dhcp: Subnet-Mask = 255.255.255.0
09:43:58 dhcp,debug,packet dhcp: Broadcast-Address = 10.11.1.255
09:43:58 dhcp,debug,packet dhcp: Domain-Server = 10.11.1.250
09:43:58 dhcp,debug,packet dhcp: Router = 10.11.1.250
09:43:58 dhcp,debug,state dhcp: dhcp-client on ether1 entering <requesting...> state
09:43:58 dhcp,debug,packet dhcp: dhcp-client on ether1 sending request with id 524268713 to 255.255.255.255
09:43:58 dhcp,debug,packet dhcp: flags = broadcast
09:43:58 dhcp,debug,packet dhcp: ciaddr = 0.0.0.0
09:43:58 dhcp,debug,packet dhcp: chaddr = 74:4D:28:78:32:ED
09:43:58 dhcp,debug,packet dhcp: Msg-Type = request
09:43:58 dhcp,debug,packet dhcp: Server-Id = 10.11.1.250
09:43:58 dhcp,debug,packet dhcp: Address-Request = 10.11.1.249
09:43:58 dhcp,debug,packet dhcp: Parameter-List = Subnet-Mask,Classless-Route,Router,Static-Route,Domain-Server,NTP-Server,CAPWAP-Server,Vendor-Specific
09:43:58 dhcp,debug,packet dhcp: Host-Name = "rb04"
09:43:58 dhcp,debug,packet dhcp: Client-Id = 01-74-4D-28-78-32-ED
09:43:58 dhcp,debug,packet dhcp: dhcp-client on ether1 received ack with id 524268713 from 10.11.1.250
09:43:58 dhcp,debug,packet dhcp: flags = broadcast
09:43:58 dhcp,debug,packet dhcp: ciaddr = 0.0.0.0
09:43:58 dhcp,debug,packet dhcp: yiaddr = 10.11.1.249
09:43:58 dhcp,debug,packet dhcp: siaddr = 10.11.1.250
09:43:58 dhcp,debug,packet dhcp: chaddr = 74:4D:28:78:32:ED
09:43:58 dhcp,debug,packet dhcp: Msg-Type = ack
09:43:58 dhcp,debug,packet dhcp: Server-Id = 10.11.1.250
09:43:58 dhcp,debug,packet dhcp: Address-Time = 86400
09:43:58 dhcp,debug,packet dhcp: Renewal-Time = 43200
09:43:58 dhcp,debug,packet dhcp: Rebinding-Time = 75600
09:43:58 dhcp,debug,packet dhcp: Subnet-Mask = 255.255.255.0
09:43:58 dhcp,debug,packet dhcp: Broadcast-Address = 10.11.1.255
09:43:58 dhcp,debug,packet dhcp: Domain-Server = 10.11.1.250
09:43:58 dhcp,debug,packet dhcp: Router = 10.11.1.250
09:43:58 dhcp,debug,state dhcp: dhcp-client on ether1 entering <error> state
09:43:58 route,debug,calc dhcp: Begin calculation
09:43:58 route,debug,event dhcp: Added candidate route
09:43:58 route,debug,event dhcp: dst-prefix=0.0.0.0/0
09:43:58 route,debug,event dhcp: attributes
09:43:58 route,debug,event dhcp: protocol=DYNAMIC
09:43:58 route,debug,event dhcp: distance=1
09:43:58 route,debug,event dhcp: scope=30
09:43:58 route,debug,event dhcp: target-scope=10
09:43:58 route,debug,event dhcp: next-hop= address=10.11.1.250
09:43:58 route,debug,event dhcp: vrf-iface (1)=ether1
09:43:58 route,debug,event dhcp: origin-type=DYNAMIC
09:43:58 route,debug,calc dhcp: Select route
09:43:58 route,debug,calc dhcp: dst-address=0.0.0.0/0
09:43:58 route,debug,calc dhcp: attributes
09:43:58 route,debug,calc dhcp: protocol=STATIC
09:43:58 route,debug,calc dhcp: distance=1
09:43:58 route,debug,calc dhcp: scope=30
09:43:58 route,debug,calc dhcp: target-scope=10
09:43:58 route,debug,calc dhcp: next-hop= address=10.11.1.250
09:43:58 route,debug,calc dhcp: comment=
09:43:58 route,debug,calc dhcp: origin-type=STATIC
09:43:58 route,debug,calc dhcp: End calculation
09:43:58 route,debug dhcp: Begin redistribution
09:43:58 route,debug dhcp: Skip update 0.0.0.0/0
09:43:58 route,debug dhcp: End redistribution