Until a sufficient number of reasonable objections and uncertainties have been met.
"A sufficient number"? So you think you've met your burden of proof even when reasonable objections to your argument remain unanswered, just because you've answered "a sufficient number" of other objections?
You get to determine what is reasonable and sufficient for you. I think that is the way it works in practical application.
Between you and me, we may reach an agreement on what is reasonable and sufficient. Or we may not.
... though as I've said several times, a standard for what's "reasonable and sufficient" that's so low that it allows through mutually exclusive claims is demonstrably too low. Reasonable disagreement about how much is "sufficient" is only possible above this level.
What I think is reasonable and sufficient is a personal experience with God of such a nature that you become convinced of God's existence.
... while I think personal experience is a generally poor form of evidence. It's based on a sample size of one (i.e so unreliable that we can't even apply statistical tools to figure out how unreliable it is) with no blinding, controls, or opportunity to test repeatability.
Personally I wouldn't expect you to accept anything less. Obviously there is no evidence or proof that I would be able to provide. You lay this burden of proof at my feet that per my own requirements, I already know I can't meet.
Do you think it reasonable to ask for a level of proof we both know I can't provide?
If the level of proof is justified, then yes, it's reasonable. Burden of proof is established based on what is needed for a conclusion to be reliable; it's not based on what you feel comfortable meeting.
If you don't have enough money for something you want to buy, you don't just plunk what money you do have on the counter and take it anyway. The price is the price, and if you can't afford it, then you just have to go without.