Sybase can only have one active statement handle, but will transparently clone a database handle when necessary (unless you set the "I don't want that" flag).
This means you may run into issues like deadlocks if you're, e.g., inserting in the same loop that you're selecting and fetching in (or other strangeness from having two separate sessions).
And then I also ran into a bug where the cloned database handle didn't have the same client character set as the original (reported on the DBI mailing list).
Update: And I just noticed that the OP doesn't mention Sybase anywhere...so this point may be moot anyway...