Not on my linux box at the moment, but try adding 2>&1 to the end.
./reaper & > mylog.log 2>&1
hmmm... thanks for the reply, but I gave that a try and I'm still getting the same results.
Woops. K, had to run downstairs and check on my headless box.
It's:
./reaper | tee my.log
At least, it works with my cgminer script, assuming it does the same with Reaper.