How and when the AI wants peace is a bit of mystery. I'd wait for them to ask for it, though. They're usually willing to give up a planet when they do.

Just fought a major war as Terrans against the Krynn. Crippling level, gigantic, tons of minors, anomalies etc. It took forever. As the Krynn sailed about destoying starbases (which were always restarted a turn or two later) I knocked out their central worlds, captured their home world and they LOL'd my Peace Offers. I offered dang near everything to them - tech, cash, planets, influ - no dice. My war machine slowly at first - then faster and faster - annihilated them. There is no more Krynn civilization anymore. Only at the end were they hot for Peace.

Just wondering if the Military value plays into the AI's consideration

Qrtxian is right. The AI will pretty much only considerss: whether it hates you forever and ever (peace is impossible), your respective military strength (very important), whether it has other wars and considers your war low priority (increases chance of peace). This leads to situations where the AI may be losing the groundwar (this is in fact likely, the AI is not effective at taking planets in large maps, a skilled human player with a puny fleet can win wars against titanic opponents this way), but is painfully oblivious to it due to "space superiority". On the other hand, making the AI consider recent planet gains/losses would lead it to sue for peace much to easily (a surprise attack taking a bunch of planets but expending much of the player fleet could become a glorious victory while in reality the AI was just about to turn the tide of war). It's natural that the AI would assume that its space superiority would lead to success in the long run, no matter the previous experiences during the war. It's only because it lacks effective groundwar tactics on bigger maps with more planets that it's self-assessment of how the war is going breaks down, causing it to laugh at perfectly reasonable offers of peace.

Equal military ranking just doesn't seem to cut it in negotiations. The AI only starts to be suitably impressed once your military rating significantly outshines theirs.