What is your site’s URL? If you have a custom domain, you may want to consider using Cloudflare.
Using backup scripts in general isn’t advised, as they use a lot of server resources- especially if they have to break a file that large into multiple pieces (compressing all of those files into a single zip takes quite a few resources on its own). A better option is to simply use Filezilla to download all of your site’s files. This won’t use any of your account’s daily resources, is far more stable, and won’t count toward your account’s storage limitation.
Hitting the daily limits usually just leads to the offending hosting account being temporarily suspended for a day. That happening repeatedly can lead to the account being permanently deactivated, however.