You're running out of memory. Is there any value in the BLOBTempStoragePath property of the data flow task? If not then try to add one with adequate storage - this won't result in the fastest performance but when the memory runs out the BLOB data will "spill" to disk in the location specified.

Have a read of the following document to see if it gives you any ideas in how you can streamline your package:

https://technet.microsoft.com/library/Cc966529

Without knowing the exact details of your SSIS package it's difficult to ascertain where this memory pressure is coming from. Like I said though, that link may provide answers.