moby: Can't run new containers - grpc: the connection is unavailable.

Description

I have to restart docker every day or so, to be able to start new containers. I think these errors started happening recently after upgrading docker.

$ docker run -i -t busybox bash
docker: Error response from daemon: grpc: the connection is unavailable.

Steps to reproduce the issue:

1. Wait a random time?
2. Run container and get grpc: the connection is unavailable.
3. Restart docker systemctl restart docker
4. Run container successfully

Output of docker version:

Client:
 Version:      17.03.0-ce
 API version:  1.26
 Go version:   go1.7.5
 Git commit:   60ccb22
 Built:        Thu Feb 23 10:53:29 2017
 OS/Arch:      linux/amd64

Server:
 Version:      17.03.0-ce
 API version:  1.26 (minimum version 1.12)
 Go version:   go1.7.5
 Git commit:   60ccb22
 Built:        Thu Feb 23 10:53:29 2017
 OS/Arch:      linux/amd64
 Experimental: false

Output of docker info:

Containers: 42
 Running: 4
 Paused: 0
 Stopped: 38
Images: 13
Server Version: 17.03.0-ce
Storage Driver: aufs
 Root Dir: /var/lib/docker/aufs
 Backing Filesystem: extfs
 Dirs: 266
 Dirperm1 Supported: true
Logging Driver: json-file
Cgroup Driver: cgroupfs
Plugins:
 Volume: local
 Network: bridge host macvlan null overlay
Swarm: inactive
Runtimes: runc
Default Runtime: runc
Init Binary: docker-init
containerd version: N/A (expected: 977c511eda0925a723debdc94d09459af49d082a)
runc version: a01dafd48bc1c7cc12bdb01206f9fea7dd6feb70
init version: 949e6fa
Kernel Version: 3.16.0-4-amd64
Operating System: Debian GNU/Linux 8 (jessie)
OSType: linux
Architecture: x86_64
CPUs: 2
Total Memory: 3.826 GiB
Name: intranet
ID: VW6E:AS3L:73N3:WXH7:3DNF:YXOQ:G7AP:T2YD:ZXMJ:JY5F:24NG:3KSI
Docker Root Dir: /var/lib/docker
Debug Mode (client): false
Debug Mode (server): false
Http Proxy: http://user:pass@10.101.0.20:3128/
Username: ...
Registry: https://index.docker.io/v1/
WARNING: No memory limit support
WARNING: No swap limit support
WARNING: No kernel memory limit support
WARNING: No oom kill disable support
WARNING: No cpu cfs quota support
WARNING: No cpu cfs period support
Experimental: false
Insecure Registries:
 127.0.0.0/8
Live Restore Enabled: false

Additional environment details (AWS, VirtualBox, physical, etc.):

OS: Debian GNU/Linux 8