I don't have examples to pluck but a decision like this comes up often in play. Generally, I'm one of the first to abandon the midpoint when it's called for. As many have noted here, it is better for the race and in a lot of positions you're likely to give up the midpoint next turn. Also in most of these positions if you don't give up the midpoint you will be leaving yourself with a shot leaving 61 or a poor 51.
So why did I go wrong here and play 8/3 6/2? Well, of the things I noted above we have some major changes. First, we have a good 51 and 61 to play as we will spring our back checker. Also, while we aren't out of the race we are trailing more by more than the usual amount when this kind of play occurs so keeping in the race I didn't think was as important. Lastly, with any luck, we won't have to abandon our midpoint. We'll roll any six, a 51, or some other small combination that allows us our next turn to also try to escape our back checker. If this happens, we will have a few more turns to maintain contain via our midpoint.
Where did I go wrong then? The attack variations where my opponent throws some of his best rolls and I start my Michael Jackson impersonation. This is where I'll wish I would have played the pips down from the midpoint to cut down on my gammon losses. Another small variation that contributes to the pool is where my opponent points on me and I enter from the bar with an awkward number like 61, 51 or even 41 or 43. The bottom line answer to this problem that I was looking for was 'gammon losses'.
My play, 8/3 6/2, comes out ahead at dmp.
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| XGID=---ABCC-A---dB--B-cdbb-A--:0:0:1:54:10:9:3:0:10 | ||||
 to play 54 | ||||
is eXtremeGammon| 1. | Rollout1 | 13/9 13/8 | eq: -0.850 | |||
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| 2. | Rollout1 | 8/3 6/2 | eq: -0.872 (-0.022) | |||
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| 1 5184 Games rolled with Variance Reduction. Dice Seed: 21140344 Moves and cube decisions: 3 ply | ||||||