I had a similar problem. My buffer could not allocate sufficient amount of memory and execution was failing. The package structure may be different than yours, but I had a massive data flow that took in an XML and loaded it into a wide table.
I've tried braking the data flow into multiple ones, changing the DefaultBufferSize, limiting SQL Server memory allocation, and it turned out to be the DefaultBufferMaxRows property on the data flow. I believe that default is set to 10,000 and I changed it to 1,000.