Short answer - Oh wait, this is debian with it's excellent buglist, searching for mate-menu yieldshttps://bugs.debian.org/cgi-bin/bugreport.cgi?bug=813130
examination of /var/log/dpkg.log and apt-cache showpkg mate-menu might help. For apt-cache especially look at dependencies and reverse dependencies.
It sounds like an upstream bug, so going to mate specific sites with bug lists is a good bet. The further upstream the better.
I believe that LMDE and Mint specific sites are still with sysvinit and not sytemd. I have no idea what services mate has running with systemd. I have no idea if mint and LMDE are going to transition to systemd or the state of systemd integration with mate. If they are not, there will be occasional problems in testing with mate in Debian testing and every other linux OS that uses systemd (over 90% use systemd).
"sudo journalctl -b -0 | grep mate"
"sudo systemctl status | grep mate" Then you can examine individaul services status
For me an example of my lxqt
axmurder@fubar:~$ sudo systemctl status |grep lxqt
│ ├─10170 lxqt-session
│ ├─10196 /usr/bin/ssh-agent /usr/bin/dbus-launch --exit-with-session startlxqt
│ ├─10199 /usr/bin/dbus-launch --exit-with-session startlxqt
│ ├─10222 pcmanfm-qt --desktop --profile=lxqt
│ ├─10224 lxqt-panel
│ ├─10301 plank --name lxqt
│ ├─13865 grep lxqt
DO NOT go to unstable - sid. Imho your options are to
1. Install a backup desktop environment , maybe xfce, for when mate has problems
2. Wait and continue to search for answers
3. Use dpkg to reinstall old versions. Transitions happen in testing and unstable. You will need to read up on this. Doing this wrong can make things a lot worse.
search engines are your friends, peace out