On your Oracle version I suggest keeping the listener.log file small in size. Generally speaking it is mandatory the listener.log file be less than 2GB in size in releases prior to 11g.
Not doing so results in process instability, random crashes, and random hangs.
To avoid that I suggest upgrading DB to minimum 22.214.171.124 (better to 11gR2). If not possible, to at least 10.1.0.5.
-- Kirill Loifman, dadbm.com
The listener.log is only APPENDED to (at the end of the file). So, yes, this can become an issue.
You should regularly reset the listener.log by deleting it.\
It will be recreated automatically, or you can create an empty file
(touch on Unix, and echo " " > listener.log on Windows)
Senior Oracle DBA