Snapshot Managed Backups will not work

I am coming back after our chat this morning, about the fact that I can no longer use the managed backup feature in Snapshot.

I asked my host to modify the php.ini file. Here is their answer:

We can set the max execution time to 300 temporarily but we can’t leave it like so indefinitely. We also can’t switch off the open_basedir php option for any website.

Is there any way you can help me.