There are a handful of reasons to close and reopen a filehandle repeatedly:

• you have another process reading the file while you're writing it
• you want to be really extra sure you get partial output safely to disk in case the program doesn't complete
• you have to reopen the filehandle redirected from or to multiple sources or destinations over the course of the program

If none of these apply, you can save some cycles by leaving it open. You may save a small bit of memory while it's not open. Whether either of these is worthwhile to worry about I can't say without measuring. I doubt this is a matter of any concern unless you're closing and reopening in a tight loop.