If it does not target an enemy, it will not break stealth (except using glowies, of course)
What powers do you normally run?
What enemies? Rikti Drones for example don't have +Perception, but they do ignore stealth values.
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Are you having a problem with a particular villain type such as sniper class Nemesis or rikti drones as mentioned above?
It sounds like you already have a good grasp of the mechanics of stealth but for anyone who doesn't, I think it works like this:
1) Each type of bad guy has a perception range. They will attack any unstealthed hero of the proper level that wanders into range.
2) Some types of bad guys like snipers have a much larger perception range.
3) If you have +stealth, it essentially reduces the perception range of most bad guys. You will be able to get very close to some bad guys but others still may be able to see you from a reduced distance.
4) Some bad guys like rikti drones are unaffected by your stealth.
I don't think hasten will break stealth but I think superspeed's stealth element is only effective while you are moving. In other words, a bad guy may not notice you running within 5 feet of him but he may notice you standing within 5 feet.
Please feel free to correct any mistakes I may have made in the above statements 
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Does activating non-attack powers negate stealth for awhile.
Specifically, one of my characters has superspeed and the celerity +stealth IO, but sometimes, enemies that don't have increased perception see me anyway. I'm suspicious that it might have something to do with hasten being on auto-activate, and it taking down my stealth.
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Turn on your combat attributes monitor and watch your stealth value. As others mentioned, it shouldn't suppress, but at least you'd be able to confirm that you were back in stealth if it was suppressed by another action previously.
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Just to add to it..
If one of the mobs sees you and reacts he often has the effect of 'pointing you out' to the others.. Soon they can ALL see you.
Bosses/LT's with a higher perception range are GREAT at 'pointing you out' to the minions standing around them.
As are the aformentioned Rikti Drones who can always see you in their perception range. <uhhh.. beep.. beep.. Boss???>
-Dragons
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The most noticeable incident recently was on an STF I was doing. We were in the thorn tree mission, and I was stealthing to the tree room to TP the rest of the party. I made it past 90% of the map just fine, but just a short way from the entrance to the tree room, all of a sudden a whole spawn of CoT just opened up on me and killed me. I'm pretty sure none of the CoT enemy types have increased perception, and I hadn't had any trouble with any CoT earler on in the map, and I was running into them frequently in the tight tunnels there. It wasn't the room with the rogue isles villains either, I made it past that room fine as well. The only powers I was running at the time were superspeed, rock armor, and hasten on auto-activate.
I always thought the CoT Boss Mages had better perception.
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Ambushes tend to 'break' the rules of stealth. The only way to avoid being 'seen' is have somebody else closer to their spawn point. 
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The Dang tree has an INSANE range of perception but it doesn't 'share' with CoT's..
CoT bosses have better perception than the lt/minions so you could have gotten lucky going through the tunnels and just not ran into any bosses.. Depends on HOW you were stealthed the -per benefit you get.
-Dragons
"I burn my candle at both ends, it will not last the night. But Ahhh my friends and Ohh my foes it makes a lovely light!"
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I always thought the CoT Boss Mages had better perception.
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They should have normal boss level perception, which is 54', IIRC. The OP mentioned Stealth IO and SS, which should give 65' stealth.
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I like COT missions because they are always easy to stealth. They don't see invisible in my experience.
Is it possible you caught some splash damage when passing by the Rogue Island Villains battle, suppressing your stealth?
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I haven't done the villain respec in a long time, but I do know it's on an Oranbega map. My guess is that he got clipped by a red crystal, sustaining damage. This might have caused his stealth to suppress and he didn't realize it, running into some ghosts who promptly attacked him.
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Ambushes tend to 'break' the rules of stealth. The only way to avoid being 'seen' is have somebody else closer to their spawn point.
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This actually depends on how the ambush is set.
Some ambushes are set to go after you no matter where you move after the triggering. These ones will see through any amount of invisibility and no matter where or how far you run they will keep coming.
Others are just set to go to the location where you were when they were triggered. With these you can easily move out of range or get behind something and once they have arrived you can sneak up to or past them unnoticed.
Does activating non-attack powers negate stealth for awhile.
Specifically, one of my characters has superspeed and the celerity +stealth IO, but sometimes, enemies that don't have increased perception see me anyway. I'm suspicious that it might have something to do with hasten being on auto-activate, and it taking down my stealth.