We've had an error
Autogrow of file 'MyDatabase_dat' in database 'MyDatabase' was cancelled by user or timed out after 30078 milliseconds. Use ALTER DATABASE to set a smaller FILEGROWTH value for this file or to explicitly set a new file size.

I was able to fix the issue  using:
ALTER DATABASE MyDatabase
MODIFY FILE ( NAME = MyDatabase_dat, size=5000MB)

We should follow the best practices from MSDN article "Considerations for the "autogrow" and "autoshrink" settings in SQL Server"   
In particular, use alerts or monitoring programs to monitor file sizes and grow files proactively. To reduce the possibility of running out of space, you can monitor the Performance Monitor counter SQL Server: Databases Object :Data File(s) Size (KB) and set up an alert for when the database reaches a certain size.

MSDN Article PRB: A Timeout Occurs When a Database Is Automatically Expanding    has a few issues: Is it applicable for SQL 2005and 2008? If not,what are corresponding articles?It's not clear, that "Expand the database manually." is the recommended method.There are no examples of the ALTER DATABASE statement.

Update: to investigate why the DB has too much space, see my post Stored procedure to find the biggest tables in the database