This sounds like it could be related to KB 883656.  I have seen this at a client site, where AS would restart itself every 20-30 seconds, and you will see the state cycle in Service Manager.  

There is a hotfix for this bug, and it is also included in the new SP4.  In order to recover from the corrupted state to allow you to apply the service pack, you'll need to do the following:
           1)       Using the SQL Server Service Manager, select the MSSQLServerOLAPService in the second (Services) drop-down list.  Uncheck the Auto-start service when OS starts box.  

2)       Close the Service Manger.  Reboot the server to get the restart process to stop looping.

3)       Rename the data folder where Analysis Services stores its databases.  By default, this is c:\Program Files\Microsoft Analysis Services\Data but it may be different on your system, particularly if there are alternate drives.  The folder in question will have subfolders along this structure:
 Data
        MyASDatabase
            MyCube1
            MyCube2
            MyCube3
and these lowest level folders will have the many data and aggregate files for each cube inside them.

4)       Create a new folder in the same directory called Data

5)       Restart Analysis Services through the SQL Server Service Manager by selecting the MSSQLServerOLAPService in the second (Services) drop-down list and clicking the Start icon.  Also, check the Auto-start service when OS starts box.  Close the Service Manager.

This should get your instance back to normal, the cubes will rebuild from the stored metadata next time that you use them.  You will need to reprocess.