What determines the minimum profit a trader demands?

A caravan arrived at my fort and I selected goods from both sides (theirs and mine) so that it showed the caravan merchant making a small profit, something like 15 on 500-worth of total traded goods. He refused my offer, so I tried upping it a couple times, by small amounts. He refused each time, then decided to stop trading with me.

Is there a way to figure out what minimum profit a merchant will tolerate without running this risk of losing the chance to trade?

What usually works for me is starting from a 100% profit ratio (e.g. you buy for 500 and sell for 1000) and gradually lower that during a trading session to somewhere around 50% (buy for 500, sell for 750). The happier the traders are, the more stuff they bring next time.

I tend to overshoot the required profit quite far, since I need to get rid of all those mugs taking up precious barrels :-)

Honestly: after the first year, you can empty most caravans if you've got a Stonecrafter working full time!

50% profit works for me all the time. If I want to buy 1000 worth of goods I offer 1500.

As the broker gets more experienced and the trader happier, I can sometimes get away with offering less, like 1400 worth of goods offered. But the trader will usually make a counteroffer that brings my offer to 100% markup and then I have to find the extra items, remove them from the offer, and add a few more items to my offer that bring it up to a reasonable price.