After some changes in monodevelop refactoring stopped to work on Linux. After some investigation I found a way to enable it back.
For Monodevelop v 5.11 (compiled from sources)
Right click on the solution, remove check near "Enable refactoring" menu item (it is located under "Options" menu item) and then set the check again. After these manipulations refactoring starts to work.
For Monodevelop v 5.9.6 (installed from Xamarin repo)
Unfortunately, "Enable refactoring" checkbox is available only in the latest Monodevelop and does not exist in Monodevelop 5.9.6, but it can be enabled manually.
Close your solution in Monodevelop. Go to your solution folder, open <YourSolution>.userprefs file then add the attribute RefactoringSettings.EnableRefactorings="True" to the first XML element "Properties" the file.
It should look like this <Properties StartupItem="...." RefactoringSettings.EnableRefactorings="True">
Then save the file and open solution in monodevelop again. Refactoring is working now