Correct, he could have tried that, but did nothing for 21 minutes. I think I gave him more than enough time to figure that one out, but he wasn't bright enough to do that. Or he was being a jerk and hoped I would get tired of the shuffling and give up. What a joke decision...
First of all, you showed us evidence from 2:56 to 3:15, so at most 19 minutes, not 21.
Second, the loss of a miner in the late game like that is not just a "mere" one piece, MTR. We see your miner at 2:56, but not in the next screenshot at 3:08, so we cannot assume when it was exactly lost. If it was lost at 3:02, for example, you wouldn't have ten minutes on the first refusal. If it was lost at 3:08, then you wouldn't have ten full minutes on the 2nd refusal at 3:13 when the 3rd refusal occurred.
All we know for certain is that at 3:08 (when we know for sure you have lost the miner), you were in a losing position and by 3:13 we have only seen five minutes of evidence of draw refusal. Had you continued on for a full ten minutes after 3:08 to the 3rd refusal, then you would have had a case. But with only two pieces left in this game you were in a clearly losing position, particularly with your opponent having a scout to force your colonel to remain near the flag opening. In fact, in the defeat screen we can see a piece has moved past your captain. We don't know the identity of that piece but cannot assume it is not the miner.