Please don't advise people to use compatibility mode, as that is
not recommended
There is nothing to "fix", that is intended behaviour, not a bug.
Messenger Plus! Live's install removes compatibility mode as it can cause problems.
The reason it doesn't restart WLM after an update is because the Messenger Plus! Live install runs with elevated (administrator) priviliges....and if it automatically started WLM then that too would be run as administrator and that shouldn't happen.
And the compatibility mode has already been explained