Why doesn't the AI invade me when at war?

Well, I guess the AI isnt as stupid as I thought.  It shouldnt be attacking you deep into your territory (invasions), if military strength is equal, not to mention if theirs is below yours. Even if their perceived military is much stronger than yours, current AI tactics make their military strength very ineffective.  

If your military is stronger than theirs, you can always be the galactic a-hole and DOW and invade them.

Oh they do try to invade my planets right up till one of my battle fleets turns up and blasts them back to kingdom come! well most of the time? I have lost the occasional planet or three!...lol

They do. Just not as often as they should. 

I've lost the occasional planet because the AI snuck a transport ship into an undefended planet when I wasn't paying attention. 

That's not really the same as the AI actually taking a large fleet into your empire.

EDIT: Speaking of large fleets, has anyone actually noticed the AI building large fleets? The fleets I have met so far haven't been very big.

Well, here's what happened to me. The Altarians were in first place and I had climbed (over the broken bodies of Yor and minor races) to second. So of course they declared war on me. I didn't have a big navy but I had been researching the pieces for a great new design (prototype missile + Harpoon, prototype elerium beam, 1 of each defense and two Ion engines on a sesame seed - um, on a medium hull). They were already at war with the Krynn (WWI-style meatgrinder) so I traded some techs and brought the Thalans in too, cranked up the industrial machine and set it to build twenty frigates (medium hull; I had lots of elerium and anti-matter) plus lots of a standard destroyer design (small hull).

I finished off the Yor and continued through that space to a group of three Altarian planets in two systems. Took the first single planet then waited for my transports to come up. While my sensor barge (I call them Sensor PLATforms - SPLATs - because that's what they do if you shoot at them) was crawling forward the sneaky AI came through the zone I couldn't see into, retook the planet and dropped garrison ships on all three. Then he built a new shipyard just out of my range and blew up the mining starbase that let me get to the first system. Cue screams of rage and disbelief.

Grrrrrrrrr. Long wait while I bring up more warships, more transports, constructors to rebuild the mining base. Then, once I had what I needed - and my SPLAT had come up so I could see - I rolled over all three.

I did notice the AI counter-invading (though not enough), making fleets of 4 or 5 large hulls, and using enough engines to get his big ships up to a speed of 9. I hadn't realized how much I was depending on the AI to only move at a speed of 3 while I moved at 10...

So well played, electronic admiral; well played. I did take you down in the end (took 5 planets and he accepted a peace deal) but you kept me snarled up for a long time with very small forces of your own, and 'playing for time' is a very human thing to do.

Have you ever considered reading some of the other threads on the forum, where this exact thing is being discussed over and over?

The AI is very, very bad at warfare. It can't build fleets properly at the moment (seemingly through a bug in the hardcode), and it struggles to put together any invasion at all. I've run a few dozen soaks now, and generally speaking it's unusual for any AI to take over more than 4 worlds by invasion, even aggressive ones, and even with improved strategies to make them more productive. In vanilla, with the 1.03 AIs, it's hopeless, since it can't even build up enough production to really put a serious fleet into space.

Speaking of AI, does it cheat or play by the same rules as the player? Also is the AI more likely to invade on certain difficulty levels?

On normal, it plays by the same rules as the player. On difficulties above normal, it gets bonuses. And no, the AI remains pretty passive even on higher difficulties.