Concurreny update error when using SSIS
This doesn't seem to be specifically an SSIS problem.

It seems to me that the logic of the original code is such that the if the previous update statement updates 0 rows that it indicates a concurrent update took place.

I'm guessing that the update statement includes one or more extra columns in the where clause on which previous values are matched. The update affecting 0 rows indicates that a concurrent update took place.

You'll need to show us the rest of the procedure to determine whether this is the case.