you are not bidding your maximum if you are 'fed up with last minute bidders'

if you bid your maximum you are willing to pay, and a last minute bidder bids MORE, he wins, and you couldnt afford it

if you bid your maximum you are willing to pay, and a last minute bidder bids LESS, you win.

it is always, but ALWAYS, the bidder with the most $$ bid that wins, irrespective of when they bid.  if your maximum is $105 then dont bid $100 and hope to not get outbid.