Scott:

"The enemy's gate is down" means "think outside the box". It means "if you remain oriented the way you were before you entered the battle you will lose." Bean reminds Ender to think this way, which is what wins the final battle. 

Bronwyn:

Ender eventually regrets his xenocide. He regrets concluding that buggers were "the enemy" when he really had no understanding of them. Thus, he lowered himself (went "down") when he attacked them (went to their gate). People lower themselves when they see others as "enemy" without understanding. I felt "Speaker for the Dead" was a confirmation of that idea, rather than a book on a whole new idea which was not a major theme of EG.

Libby:

Or does it mean that it's easier to 'fall' into seeing someone as your enemy than it is to meet them on your own level- as equals? And that this is a mistake we should avoid? 

Nick: 

I think that it's just a nifty tactical move in zero G combat. It kind of makes it easy, just fall towards the enemy's gate and take over. Besides, that's basically the tactic that was used in the last battle, even though he didn't have a single fighter left to "go through the gate", but that's ok being as the gate was an expanding matter disruption... 

Scott:

In the final battle he decides "If I break this rule, they'll never let me be a commander. It would be too dangerous. I'll never have to play a game again. And that is victory." It is paradoxical that in the very act of opting out of future command of the fleet he obviates any future command, but he's still quitting. 

Later:  

I need to clarify that the rule he is breaking isn't "the enemy's gate is down",  but the rule about going through the gate without wiping out all the enemy first, just like he did in the final battle at Battle School.

Scott:

BTW, "the enemy's gate is down" represents OSC's acknowledgement that zero G battle will require taking 3-dimensional thinking to yet another level. 

Pg:

I think that I'll add that to Ender, at that time, it was a reminder to himself and the other children that "this is just like the Game" or "it is only a game". 

Pg:

To Bean, it possibly meant that it was time to give up, to stop playing the game. Paradoxically however, he was the only child who was aware that it *wasn't* a game. So I'm not exactly sure I accept this explanation as its written in the text.

Scott:

As a student of military history and tactics, OSC shows in EG that he knows that in military parlance you attack the enemy's "center of gravity". Where in the Battle Room was the enemy's "center of gravity"? His/her gate. Ender and Bean proved that conclusively in their final Battle Room battle. Direction of gravity: down. The enemy's gate is down.

Time for a gut-wrenching admission: sycophant that I am ... ;-d ... the only major fault I've ever picked with EG is that even as I read it the first time I kept thinking, What is the objective here? Why aren't they attacking and defending the gates? Attrition is the aim of the Game?? They're teaching these kids that the only way to win is to attrit the enemy??? I was greatly relieved when the attack on the gate prior to attrition finally came, but thought commanders worth their salt would have thought of it long before, even if only once, and even if it meant the rules were changed immediately, the way Anderson did when Ender finally pulled that trick. 

Carlos:

I think down only has negative connotations when it is in a certain context, and that it is possible to look too much into something. I think that has happened here, and happens quite often. We try and find meaning where there is none, rather than simply taking something at face value, sometimes in an attempt to make something we believe is great greater (not necessarily a conscious decision), or I am sure for other reasons. 

The red baron:

I think it just started off as a good strategy move. You cannot fight if you don't know how to get to your goal. When It was used in the final battle against the buggers, I think it was just a joke that Ender used to remind them that they are only kids, and can still have a good time.

The red baron:

just a little thought on that "gate is down" stuff. if the gate is down, then you are falling towards your enemy. In millitary history, armies fight better when they have the high ground, because they can run towards them very fast, and the other side has to run up hill to fight them, slowing them down. Ender might be playing on the sub-counceise (can't spell for any thing, you know, the sub-mind, like when we sleep) so his solder's moral is boosted. Who knows?

Pg:

Certainly there is a psychological advantage to perceiving yourself as engaging in battle from higher ground. 

Scott:

It's a lot more than a psychological advantage. Not only is the high ground the advantageous position for a hand-to-hand battle as rb pointed out, but every projectile weapon from the human-thrown rock to the Star Wars missile defense system is put in an advantageous position the higher it is placed, both for offensive and for defensive purposes, in that effective range and coverage are multiplied by altitude. Commanders have always aimed to seize the high ground and are advantaged when they have it and disadvantaged when they don't -- hence the term "fighting an up-hill battle."

Bronwyn: