Is your hosting linux based? do you have console access to it?
If you have some basic linux knowledge you can write a shell script to do a backup and set it to run automatically with a cron.
1-The shell script would contain a command to create a zipped file with the content of your website. You can easily do it with the tar command.
2-The cron will schedule its running time, and you can modify it according to your needs. Your control panel should have tools to create cron tasks, but if not, you can still do it by editing your crontab file.
If you don't know linux, your hosting support should be able to do it in no more than half an hour of work, it might be worth asking them to do the job for you, even if they might bill you a couple more bucks at the end of the month.