Snapshot issues with shared host and larger backups

I have been having issues with full backups, probably because the backups are over 1GB and it may also have to do with limited server resources from my host. We talked about this before and I notice many other people were having similar issues.

Have you come up with a solution that works for my type of issue? I don't want to go through several trial and error steps again.

I have had this server host for a long time. Snapshot has worked in the past and it works with one of my small sites. But on the this site, it stops working locally and remotely once the site is over a couple of GBs. I don't know what the max size is for successful backups, but it seems to be somewhere between 700MB and 2GB. Hard to tell because of the way my site imports data on a daily basis.