Peace Making

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.

I find that the AI is more willing to make peace when you are more powerful than them. More so when you are clearly kicking their ass. Destroy their ships, destroy their starbases, and take their planets. Do this and they might realize that being at war with you might be a bad idea. Keep this up and they may end up asking for peace or surrendering (to someone most likely).

If you don't appear to be winning, it is possible to pay them to accept peace with you. However, I am usually quite happy to keep taking worlds until there are almost none left. I might leave them with a minor world and offer them peace in exchange for them giving me technologies (primary concern) and money (secondary concern). By minor world, I mean low PQ world that will probably culture flip to me in the near future.

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

The military rankings are pretty much the only thing the AI considers when you ask it for peace, actually. Though it might offer peace on its own if it's fighting other wars or is just tired of the conflict.

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.

I suspected as much - the 1st war i had in this game was with the Torians and they were cool for Peace when my Mil Value was equal to theirs...

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.

i almost never had A.I declare war on me, i usually try to pin the most powerful civilization in the game against every other lesser civilizations in the game so that they won't bother me as i try develop my planets. but i think the peace making is as the previous posters suggest, has to do with the military rating and the current war that they have with other A.I. crazy as it may sounds, if you utterly obliterate all A.I's ship, and offer them peace treaty with some of your latest ship, they will give you everything. i mean everything as in everything. including themselve, their wife, their children, their women, their relative, every single thing. i tried that on several civilization in obscene mode, they think that's a great deal, it has to be. because none of them ever declined.