...bring your E to the mechanic and have all of your valves adjusted. All my intake and exhaust valves were either loose or tight. Once I had my mechanic adjust them, my problem went away instantly. Its been about 6 months since he did this and still no problems.
I've been chasing the "stalling" problem for several years now. I began to notice it about 6 months after buying it (07 Element Manual Transmission) as winter approached and the weather became colder (Northeast). When starting cold, it would idle high (choke?) for several minutes. When that high idle dropped back to a normal idle of around 700-800, it would consistently stall when coming to a stop. After several minutes of driving at the regular idle, the problem would just go away until the next time the vehicle was started cold.
When this problem occurred, I noticed the RPMs doing funky things. When in gear, coming to a stop, the RPMs would be in their normal range (3K or so). As soon as I pushed in the clutch and rolled to a stop, the RPMs would come down as expected, but they came down to 500, stopped there for a 1/2 second or so, then DIP down to 300-400. At this point, one of two things happened. One, the RPMs would immediately pop back up to 700-800 and the car remained running. Or two, the car would simply stall because the RPMs were too low.
I brought this problem to Honda (where I purchased the vehicle NEW) and they couldn't find any error codes or offer any advice on the problem. They supposedly searched their database of known issues and came up blank. Every single time I brought the car in for service (free oil changes and wiper replacements) I complained about the stalling issue and made them DOCUMENT IT so at least there's a paper trail if it ends up being a warranty issue. At one point I even left my car there overnight so they could reproduce it from a cold start. They said the next morning it ran just fine and never stalled. Odd. I picked the car up and it stalled on me at the first light.

Either my luck sucks or these guys are bumbling idiots. I'm pretty positive now that it's the latter.
I came here to this forum and began investigating the problem here (and on other web sites). People talk about the throttle body being dirty, etc. But this happened on a BRAND NEW ELEMENT, so I discounted that theory.
Then I read about the valves needing adjustment (which Honda says doesn't need to happen until over 100K). So this weekend I opened up my E to inspect the valve clearances and perform a valve adjustment if necessary.
What I found absolutely floored me. I triple and quadruple checked them to be sure I was seeing this correctly.
For the record, the proper clearances are:
Intake Valves: 0.008-0.010
Exhaust Valves: 0.011-0.013
My clearances were roughly as follows (I don't have the exact clearances with me right now...they're at home):
Intake #1: 0.008 0.008
Intake #2: 0.009 0.009
Intake #3: 0.009 0.010
Intake #4: 0.009 0.010
Exhaust #1: 0.003 0.008
Exhaust #2: 0.008 0.007
Exhaust #3: 0.003 0.008
Exhaust #4 0.003 0.004
The intake valves were pretty good, but just LOOK at the EXHAUST valves!!! Not ONE of them are in spec. As a matter of fact, they are completely off!
To keep a long story going...
I adjusted them all to the middle of the spec range, buttoned it up and took it out for a spin both yesterday and today.
It hasn't stalled.
When coming to a stop, the RPMs still come down to about 500 and then rise to 700-800, but they no longer DIP down to 200-300, so it doesn't stall.
Keep in mind I'll have to drive it for a week or so to see if it REALLY fixed the problem.
But it is IMPORTANT to note that anyone with an Element should get their valves adjusted more frequently than recommended by Honda. Mine were off directly from the factory floor! Oh and I have 50,000 miles on it now.
I spoke with a different Honda place and the mechanic told me tight valves could cause the stalling issue due to vacuum problems. He also told me he would adjust the valves every 30,000 miles if it were HIS car. He said doing them at 100K is just stupid and has no idea what Honda was thinking.
Hope my writeup helps someone. I wish I would have found a writeup like this when I was trying to figure out the problem... lol Hopefully, I've solved the issue. Next valve adjustment at 80K.