Bluetooth speaker fails to reconnect when turned on (but it tries)

Bluetooth speaker fails to reconnect when turned on. Watching the Bluetooth icon in the Unity panel I can see it is trying (B icon briefly gets the expected padlock and then loses it). The speaker doesn't reconnect then unless initiated by the laptop (set Connection = ON in the panel).

Note this bug is only about the Bluetooth connection, and not about audio problems (of which there are a few).

ProblemType: Bug
DistroRelease: Ubuntu 16.04
Package: bluez 5.37-0ubuntu5
ProcVersionSignature: Ubuntu 4.8.0-52.55~16.04.1-generic 4.8.17
Uname: Linux 4.8.0-52-generic x86_64
ApportVersion: 2.20.1-0ubuntu2.5
Architecture: amd64
Date: Mon May 22 16:28:37 2017
InstallationDate: Installed on 2017-05-19 (2 days ago)
InstallationMedia: Ubuntu 16.04.2 LTS "Xenial Xerus" - Release amd64 (20170215.2)
InterestingModules: rfcomm bnep btusb bluetooth
MachineType: LENOVO 20CM0010AU
ProcKernelCmdLine: BOOT_IMAGE=/boot/vmlinuz-4.8.0-52-generic.efi.signed root=UUID=ae0f1ee2-ca1c-4a64-985f-b27f9a8c0e50 ro quiet splash vt.handoff=7
SourcePackage: bluez
UpgradeStatus: No upgrade log present (probably fresh install)
dmi.bios.date: 09/05/2016
dmi.bios.vendor: LENOVO
dmi.bios.version: N10ET45W (1.24 )
dmi.board.asset.tag: Not Available
dmi.board.name: 20CM0010AU
dmi.board.vendor: LENOVO
dmi.board.version: SDK0E50510 WIN
dmi.chassis.asset.tag: No Asset Information
dmi.chassis.type: 10
dmi.chassis.vendor: LENOVO
dmi.chassis.version: None
dmi.modalias: dmi:bvnLENOVO:bvrN10ET45W(1.24):bd09/05/2016:svnLENOVO:pn20CM0010AU:pvrThinkPadX250:rvnLENOVO:rn20CM0010AU:rvrSDK0E50510WIN:cvnLENOVO:ct10:cvrNone:
dmi.product.name: 20CM0010AU
dmi.product.version: ThinkPad X250
dmi.sys.vendor: LENOVO
hciconfig:
 hci0: Type: BR/EDR Bus: USB
  BD Address: 34:02:86:EE:0F:47 ACL MTU: 1021:5 SCO MTU: 96:6
  UP RUNNING
  RX bytes:1298997 acl:147 sco:25046 events:1846 errors:0
  TX bytes:1750802 acl:1411 sco:18166 commands:299 errors:0