Package components randomly failing

I have a package with several data flow task. These task are failing, as far as I can tell, based upon the phase of the moon and the position of Mars. Everytime something fails I get the same message.

SSIS Error Code DTS_E_OLEDBERROR. 
An OLE DB error has occurred.
Error code: 0x80004005. 
An OLE DB record is available. 
Source: "Microsoft SQL Server Native Client 10.0" 
Hresult: 0x80004005  Description: "Syntax error, permission violation, or other nonspecific error".

"component "[insert component name]" failed validation and returned validation status "VS_ISBROKEN". 

This is what is happening. We'll call them DFT 1, 2, and 3. DFT 2 is dependant on DFT 1's successful execution. DFT 3 has no dependancies.

1. I run the package. DFT 1 fails. DFT 3 works.

2. I fix DFT 1. I run the package. DFT 1 runs. DFT 2 fails. DFT 3 works.

3. I run the package and do nothing to DFT 2. DFT 1 and 2 works. DFT 3 fails.

4. I run the package DFT 1 and 2 work. DFT 3 fails.

5. I recreate DFT 3. I run the package. DFT 3 runs. DFT 1 fails.

6. I run the package. DFT 1 works. DFT 2 fails. DFT 3 runs.

7. I run the package. DFT 1 works. DFT 2 works. DFT 3 fails.

It's like DFT wack-a-mole.