The question I would ask is how certain are you the it’s *brand demand* that has been falling? As my brand continues, I’ve noticed that competitors bidding on similar/same keywords as my brand has increased and I’ve lost impression share.
This is an important distinction, because if it’s a matter of competitors increasing then 100% yes, absolutely increase brand presence and brand keyword bidding. But if it’s due to low/no interest and there are not an increase in competitors, then increasing brand keywords wouldn’t do much, unless I’m missing something.
Oh, and I’m assuming by “brand presence” you are referring to branded keyword Search campaigns.