I doubt this has anything to do with MATE, as MATE is just a desktop.
More likely, it is something underneath. The user-agent icon with your post says "Ubuntu." Is this MATE with Ubuntu?
I did find a thread on the Ubuntu forums about problems suspending a Toshiba, but I can't tell whether it's the same model. Maybe it will help:
If not, please post what Linux distro/version you are using and what specific model Toshiba you are dealing with.
You might also try suspending it from the command line and capturing any error messages. Here's an article on how to do that if you are using the pm-utils package, which is default for a number of Linux distros, including, according to the article, "RHEL, Fedora, CentOS, Red Hat Enterprise Linux, Debian, Ubuntu."