I find myself with two sites hosted on their servers an on both occasions Akeeba Backup works. I find the backups at the backend from time to time are failing (not sure why - ALICE points out some problems, but it seems there are other issues for Godaddy accounts), but using the frontend option combined with a CRONjob seems to be working every time, as stated earlier here: Ticket #20434.
FYI: one of those sites is 2.5.22 ... the other one 3.3.1 (both times the latest version of Akeeba Backup)
One is an older account and I need to work with :
/usr/local/bin/php "$HOME/html/cli/akeeba-altbackup.php" --profile=YOURPROFILE_ID >/dev/null 2>&1
The other account is recent and needs:
/usr/bin/php5 "$HOME/public_html/cli/akeeba-altbackup.php" --profile=YOURPROFILE_ID
Anyhow, to improve information provided to our (future) customers, I would be obliged if you could give us the reason(s) that lead to this decision.