1) Concurrency. Do you have multiple people accessing the same dataset? Then it’s going to get pretty involved to broker all of the different readers and writers in a scalable fashion if you roll your own system.
2) Formatting and relationships: Is your data something that doesn’t fit neatly into a table structure? Long nucleotide sequences and stuff like that? That’s not really conveniently tabular data.
Another example: Nobody would consider implementing software like Photoshop to store PSDs in a relational format, because the data structures don’t really lend themselves to that type of storage or query pattern.
3) ACID (sort of a corollary to #1): If Atomicity, Consistency, Integrity, and Durability are not challenges with a flat file, then go with a flat file.