The answer to your problem lies here under "Note 4":
Running DKMS in the guest OS will keep Guest Additions installed after a guest kernel update.
I believe your host machine suffers of the same problem!
I'll divide my instructions in two parts: part one for installing virtualbox and part two for installing guest additions.
PART ONE: Installing virtualbox from debian package
I just did this in a fresh Ubuntu Mate installation (much better than the basic distribution!) because Ubuntu Software Center didn't give me the latest version which is 5.1.2.
Next steps in host's terminal:
I followed this link
sudo apt-get update
sudo apt-get install dkms
Download virtualbox-5.1_5.1.2-108956~Ubuntu~xenial_amd64.deb
from link (amd64 in filename is NOT for AMD only)
sudo dpkg -i Downloads/virtualbox-5.1_5.1.2-108956~Ubuntu~xenial_amd64.deb
Errors appear so, rebuild
sudo apt-get -f install
Redundant:
sudo apt-get install build-essential linux-headers-$(uname -r)
sudo rcvboxdrv setup
- run
virtualbox
if message about errors, reconfigure with sudo /sbin/vboxconfig
Finally, add a Virtualbox
menu item with this superb tool that only Ubuntu Mate offers(!)-the all mighty alacarte
command of previous decade and broken in newer versions of Ubuntu!: System->Preferences->Look and Feel->Main Menu

PART TWO: Installing guest additions
A proper installation is described here although, the writer forget to mention that everything is being executed in the guest!!!
Even so, problems existed in my case so I mixed previous link with this and here the final steps:
Create a Ubuntu guest server graphically or use an existing one with a name, e.g. My Ubuntu Server
copy *.iso
to your guest folder My Ubuntu Server
cp /usr/share/virtualbox/VBoxGuestAdditions.iso ~/'VirtualBox VMs'/'My Ubuntu Server'
- on Virtual Box Manager (main window) select the just copied file

In the picture it's obvious that I already did it!
Next steps in the guest's terminal:
sudo apt-get update
you should have dkms
:
dpkg-query -s dkms | grep -i status
Status: install ok installed
otherwise
sudo apt-get install dkms
- now it's time to rebuild guest additions:
sudo mount /dev/cdrom /mnt
cd /mnt
sudo ./VBoxLinuxAdditions.run
reboot
- when logged again run
sudo mount | grep vbox
and in my case the shared folder is in /media/sf_shared