Trocar >
por >>
.
> = write to file, overwriting what was already there
>> = append to file, create if it doesn't exist
ou seja:
MAILTO=****@gmail.com
10,30,50 * * * * ~/webapps/****/apache2/bin/start
*/10 * * * * /usr/local/bin/python2.7 ~/webapps/****/WR/cron.py >> ~/webapps/****/WR/cron.log 2>&1