First, I have read probably close to 100 posts, watched at least 100 videos across Ford/Mazda forums with this similar problem.
I'm really hoping I can get some help from the Mazda peeps!

Problems: Sputtering, riding rough, drives great until warmed up - about 5 miles (or 15/20 min.of driving) then...

• No issues accelerating, drives great not sluggish AT ALL.
• Deceleration RPM drops then seems to bounce.
• When coming to a stop, car stalls and will not start back up.
• If I leave it for about 30 min. starts right up and drives fine.
• Rinse and repeat.
• Pending Code: P2177

Fixes I've tried so far (mostly because the car has 200k mi. on it)
New:
Gas cap
Reservoir
Spark plugs
Ignition coils
Valve cover
Hoses and water outlet
Top pass engine mount

Cleaned/replaced:
Throttle body (completely inside out - did not move throttle)/replaced gasket
Reset timing (20 min on/ 20 min. a/c)
Cleaned out intake manifold/replaced gaskets - checked hoses and shutter valve actuators
New PCV valve/hose (cleaned out oil separator)
Cleaned MAF/MAP sensor
Cleaned EGR valve
Changed oil w/filter
Flushed radiator -interior heat runs at idle (so it's been burped)

Tested brake booster (holds pedal) turn ignition off (after 30 sec it drops slightly). Tested RPM while holding brake and pumping (very slight variations in RPM)

After fixes, same continuing problems. On a budget, and have nothing but time so it's a matter of principle at this point to find what the heck it is!
If I can't figure this out, this car may end up in Tampa Bay... Any help? Please?

 

Wow... That is very detailed. I am not a mechanic but I am interested and would like to know what you find out. Good Luck!

I have a 2006 Mazda3 2.0L 5 speed sedan and recently took the battery cables off to reset engine idle. It is not dropping the RPMs very fast and seems to idle a little high right now. I have a check engine light on. Auto store said it was related to a sensor or something, like it wasn't getting driven far enough to heat up the coolant or something. I haven't been really bothered by it and the car runs very good, gets good mpg, so I haven't been overly concerned. I did read some complaints somewhere, maybe youtube, about faulty thermostats on the Mazda that could cause this and yesterday I kept an eye on my temp gauge. The gauge hardly rose above Cold , so I think I am going to try replacing the thermostat on my car.

 

That code means it's running too lean. At start up, it should be running open loop on a cold start, meaning it's going to be running rich with more fuel than after the engine is warmed up and resting at idle. After warm up, the ECU then starts using the info from the MAF and O2 sensors to adjust the fuel/air tables. When the engine is cold, the O2 readings just aren't accurate. Have you tried checking for air leaks around your intake manifold or tried removing your intake manifold to inspect that? Also, how many miles do you have on your Mazda 3 2.3? I ask because my reasoning would be that it's not getting enough fuel for how much air is going in. If there's a leak around the intake manifold, it could be taking in too much air (since the air coming in isn't being regulated by the throttle body) and the intake manifolds can get severely gummed up from oil being recirculated from the EGR valve. I tore down a 2.3 engine with 180k miles and the intake manifold was completely coated in a thick layer oil everywhere inside. The flappers you see in the picture were really coated is old oil and were sticking. After degreasing it inside and out, they were operating correctly and I still use it (with an adapter plate) on my 2.5 from a Gen 2 Mazda 3. It's surely a job to get that thing off with the engine still installed but it sounds like you know your way around an engine. For the MAF sensor, those things are really sensitive and even cleaning sometimes doesn't do the trick. I picked one up cheap used for a Subaru Outback I repaired once that was certified to work to repair a similar issue which also worked.

 

Try cleaning fuel injectors and replace oxygen sensors.