OK so we have decided that brutes are safe to use as long as you clean them. LOL..
Seems worth noting that there's nothing in the Brute to worry about. (We know millions of reefers are using them every day like this with no issue, after all.)
So, how often to clean it it simply how often it gets dirty in your environment and based on what you're doing with it.
Keeping the vat well sealed and with nothing in it like heaters, pumps, air stones, vinyl tubing (which WILL leach the additive that makes it clear.) should be all it takes to keep a vat of pure water pure and your container clean.
Any other setup will reintroduce some contaminants (air pollution, dust, bugs, etc) and sooner or later will require a clean-out due to bacterial or mildew growth.
I compromise and run a air stone and use tubing and a big submersible pump to transfer the water when/where it's needed. The tubing does turn white from clear and grow a bacterial film over time, and I'm sure there are some laundry room fumes that the air pump probably mixes into the water occasionally.
I have done one clean-out, so I guess that makes it about once every 3-4 years for me. I replace the tubing and wipe everything out with bleach water, then rinse.
That said, my next redesign will take these "issues" into account. I will use hard PVC or simply have no permanent plumbing in the RODI tank. I like having the water aerated since I believe it makes my mixed saltwater read for the tank more quickly...but I'll be testing without aeration first.
$0.02
-Matt