Same issue in Ubuntu 18.04, fresh install on Lenovo e540 notebook, with two different bluetooth mouse
 - Logitech M557
 - Tecknet BM307

The problem occurs in the following cases:
 - Mouse Switch off then on
 - Mouse inactivity (leaving the notebook for 5/10 minutes)
 - Notebook sleep
 - Notebook reboot

The bluetooth mouse can't reconnect. I have to reboot or "systemctl restart bluetooth" and run the pair again.

syslog relevant messages during notebook idle:
May  7 15:34:42 alastor /usr/lib/gdm3/gdm-x-session[1748]: (II) config/udev: removing device BM30X mouse
May  7 15:34:42 alastor /usr/lib/gdm3/gdm-x-session[1748]: (**) Option "fd" "113"
May  7 15:34:42 alastor /usr/lib/gdm3/gdm-x-session[1748]: (II) event16 - BM30X mouse: device removed
May  7 15:34:42 alastor /usr/lib/gdm3/gdm-x-session[1748]: (II) UnloadModule: "libinput"
May  7 15:34:42 alastor /usr/lib/gdm3/gdm-x-session[1748]: (II) systemd-logind: releasing fd for 13:80
May  7 15:34:42 alastor upowerd[1118]: unhandled action 'unbind' on /sys/devices/pci0000:00/0000:00:14.0/usb1/1-7/1-7:1.0/bluetooth/hci0/hci0:256/0005:0A5C:4503.0005


syslog relevant messages activating the notebook:
May  7 15:42:36 alastor bluetoothd[13044]: Can't get HIDP connection info
May  7 15:42:41 alastor kernel: [14272.937283] Bluetooth: hci0: last event is not cmd complete (0x0f)
May  7 15:42:41 alastor bluetoothd[13044]: connect error: Host is down (112)



lspci
00:00.0 Host bridge: Intel Corporation Xeon E3-1200 v3/4th Gen Core Processor DRAM Controller (rev 06)
00:01.0 PCI bridge: Intel Corporation Xeon E3-1200 v3/4th Gen Core Processor PCI Express x16 Controller (rev 06)
00:02.0 VGA compatible controller: Intel Corporation 4th Gen Core Processor Integrated Graphics Controller (rev 06)
00:03.0 Audio device: Intel Corporation Xeon E3-1200 v3/4th Gen Core Processor HD Audio Controller (rev 06)
00:14.0 USB controller: Intel Corporation 8 Series/C220 Series Chipset Family USB xHCI (rev 04)
00:16.0 Communication controller: Intel Corporation 8 Series/C220 Series Chipset Family MEI Controller #1 (rev 04)
00:1b.0 Audio device: Intel Corporation 8 Series/C220 Series Chipset High Definition Audio Controller (rev 04)
00:1c.0 PCI bridge: Intel Corporation 8 Series/C220 Series Chipset Family PCI Express Root Port #1 (rev d4)
00:1c.2 PCI bridge: Intel Corporation 8 Series/C220 Series Chipset Family PCI Express Root Port #3 (rev d4)
00:1c.3 PCI bridge: Intel Corporation 8 Series/C220 Series Chipset Family PCI Express Root Port #4 (rev d4)
00:1c.4 PCI bridge: Intel Corporation 8 Series/C220 Series Chipset Family PCI Express Root Port #5 (rev d4)
00:1f.0 ISA bridge: Intel Corporation HM87 Express LPC Controller (rev 04)
00:1f.2 SATA controller: Intel Corporation 8 Series/C220 Series Chipset Family 6-port SATA Controller 1 [AHCI mode] (rev 04)
00:1f.3 SMBus: Intel Corporation 8 Series/C220 Series Chipset Family SMBus Controller (rev 04)
01:00.0 3D controller: NVIDIA Corporation GK208M [GeForce GT 740M] (rev a1)
03:00.0 Unassigned class [ff00]: Realtek Semiconductor Co., Ltd. RTS5227 PCI Express Card Reader (rev 01)
04:00.0 Ethernet controller: Realtek Semiconductor Co., Ltd. RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller (rev 10)
05:00.0 Network controller: Intel Corporation Wireless 7260 (rev 73)



lsusb
Bus 002 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub
Bus 001 Device 006: ID 8087:07dc Intel Corp.              <-------------- Bletooth controller
Bus 001 Device 004: ID 0bda:5719 Realtek Semiconductor Corp. 
Bus 001 Device 003: ID 138a:0011 Validity Sensors, Inc. VFS5011 Fingerprint Reader
Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub