To get around this you have a couple options. Your best option would be to take backups from the Console or Command Line. When ran from the Console, PHP doesn't have any limits like time or memory; it just goes and goes until it's done.
If that's not possible, you'll have to increase your
max_execution_time setting in PHP. I can't give you a value to set,
since it's dependent on how many files, how large those files are, the
CPU and RAM available, and I kid you not, the type of hard drive on your
server (SSD vs the old spinning disk variety), so you may have to
experiment. Were it me, I'd start at 30 minutes and work my way down.
And, if setting PHP configuration isn't an option, you'll have to
get fancy with configuration. For example, be explicit about what
directories to backup. Avoid using the exclude paths if possible.
Definitely don't use regular expressions for excluding paths (that takes
TONS of time).