Fedor,
We have found issues with the tool bar button in the Servers view not reflecting the correct status of the CodeLive. A bug is filed for the dev team to work on it. Currently, the context menu action (right click on the server > CodeLive) indicates the current state for the server correctly.
Can you please check if you see the correct status for CodeLive in the context menu after the IDE restart?
Apologies for inconvenience caused.
–Swapna
MyEclipse Support