Here's the relevant bit from your log. Keep an eye on the time:
INFO |130605 16:00:02|Beginning post processing file <root>/administrator/components/com_akeeba/backup/site-www.homestest.dreamhosters.com-20130605-225838.jpa
INFO |130605 16:00:02|Preparing to email site-www.homestest.dreamhosters.com-20130605-225838.jpa to [email protected]
DEBUG |130605 16:00:02|Subject: Akeeba_backup_configuration
DEBUG |130605 16:00:02|Body: Emailing site-www.homestest.dreamhosters.com-20130605-225838.jpa
DEBUG |130605 16:00:02|-- Fetching mailer object
DEBUG |130605 16:00:02|-- Joomla!'s mailer is using sendmail mail method.
DEBUG |130605 16:00:02|-- Creating email message
WARNING |130605 16:00:02|-- Attaching <root>/administrator/components/com_akeeba/backup/site-www.homestest.dreamhosters.com-20130605-225838.jpa
DEBUG |130605 16:00:02|-- Sending message
DEBUG |130605 16:13:25|Kettenrad :: Attempting to load from database (backend)
Sending the backup by email takes 13 minutes and 23 seconds. That's way too long for the Apache timeout limit of 120 seconds (2 minutes) and it returns a 500 error.
Solution: set the "Part size for split archives" option to 1Mb. You will end up with 22 part files, each one of them being emailed to you in about 40 seconds, preventing the timeout from occurring.
IMPORTANT: Please also read the documentation regarding the send by email feature's limitations.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!