"Not enough storage" Error When Trying To Select Destination Table in SSIS

I am building an SSIS package and getting an error when setting "Name of the table or the view" in the OLE DB Destination editor.

SSIS Error Code DTS_E_OLEDBERROR.  An OLE DB error has occurred. 
Error code: 0x8007000E. An OLE DB record is available.  
Source: "Microsoft SQL Native Client 10.0"  Hresult: 0x8007000E  
Description: "Not enough storage is available to complete this operation.".

Failed to open a fastload rowset for "[dbo].[MyTable]". 
Check that the object exists in the database.

Exception from HRESULT: 0xC0202040 (Microsoft.SqlServer.DTSPipelineWrap)

But, the table is definately there.

What could be causing this error?

Try saving the package and exiting from BIDS. Then start again, and try fixing the destination component.

It's only complaining about the table because it was in the process of handling that table at the time of the Out of Memory exception. It has a one track mind about that - failure setting up table == table does not exist.