In my limited experience tolerance can build rapidly.
1/3 of a gram per day, even of exceptionally potent oil, should not knock him out for more that the first 4 or 5 days.
However, none of my patients has cancer in the liver.

Sounds like the oil is stacking up behind chemo toxins and not getting processed normally.
That's just a guess, I'm not a doctor.

I'll make another assumption here.
I sounds like that oil was derived from mostly Indica type cannabis.
If this is the case, blend in some Sativa derived oil to lessen the soporific effects.
He'll still be very stoned but will be able to stay awake and might even become animated and talkative.

Here are some links that should help;

http://boards.cannabis.com/cannabis-...nabis-oil.html.

We all owe McDawg for that thread!
Mahalo McDawg!

Any way we can help? Don't be shy.

Aloha,
Weezard