I had similar problem and here is how I fixed it.
First I thought, something was wrong with the backup-plugin so i tested other backup plugins but same php out of memory error. For example
"Database error MySQL server has gone away for query"
"Cannot allocate sufficient memory"
So I thought something wrong with php memory. Then some articles suggested to edit wordpress's .db files or some other files in cpanel, to increase memory or time limit, but those tricks didnot work out.
Finally I came to know that one of the possible reason for memory error is, your mySQL file is too big (something like more than 200MB) That's why memory runs out while doing things like backup. The culprits are following plugins-
You may be using one or both of following plugins
1. Better WordPress security
2. Akismet spam remover
both of them create 'logfiles' in your MYSQL file and over the time, because of them, the SQL file becomes very huge.
So, you've to goto phpmyadmin >> empty the tables that contain those logfiles.
Then try to take backup again and it'll run smoothly.
In my case, Better WordPress Security alone had huge logfile of 480MB inside mysql. When I emptied the "wp_bwps_log", the size of mysql file was reduced to barely 47MB (for 700 posts and 3000 comments on my site.)
And then I tried to take backup using "BackWPup" plugin and it worked smoothly without any problem.