OS 46AX

First, consider sending it to OS for a look-see. If it has excessive play in the carb then it's a manufacturing defect that they should be happy to fix.
Second, see if any of your buddies has one and go fondle their carburetor to see if it has different characteristics -- if the play is significantly different then you can _definitely_ suspect manufacturing problems.
Third, consider borrowing a carb from someone, or even a whole engine. If it's a carb problem then changing the carb should fix it. If it's a tank or tubing problem then changing the whole engine won't fix it.
Forth, go over your whole fuel system for leaks, foaming, incorrect tank placement, etc. Nothing more embarrassing than changing all the tubes in your TV before you notice that the power cord is unplugged...

I have a reasonable new 46AX myself, probably 2+ gallons through it.
Once run in, they don't seem to deadstick during normal flight at all. See my idling comment below.
New, they can exhibit some running issues but they quickly fade as the engine runs in.
As for idling, this is a sports motor and has some impressive porting. It isn't designed to idle for extended periods and will fuel up very quickly if the engine isn't given a "blip" every few seconds. 45seconds of idling is excessive, minutes is ridiculous.
Don't idle the engine excessively. Assuming it's already tuned: Start it, take to flight line, take off. For landings, cut throttle on final approach and land.
This would suggest the engine is still running in. I had some concern about the low/high transition causing a big flat spot. The flat spot faded as the engine ran in and vanished before I had a chance to pull the cowl and adjust the low end.
Have you checked it's not loose? Remember the rotor runs on helical groove, pressing on the end of the rotor will definitely change things. The end of the rotor is not expected to have any significant axial loads placed on it.
1. Give it some more time to run in, I had some concerns but they suddenly faded as I completed the second gallon. 2. I slightly tweaked the low end initially, a fraction leaner was all I needed to get it running better. The flat spot still persisted for some time but eventually vanished. 3. Don't sweat the rotor slop unless something is loose. 4. Idle speed will get better (you can consistently run a low rpms) as the engine runs in. 5. Sports engines are not designed for excessive idling. Keep idle times as short as possible and blip the throttle to keep it clear.

Pull it out and run it on the bench. See if the problem is the motor or your fuel set-up. This is the easiest and least frustrating way to zero in on the problem. Most unusual for an OS to not idle well right from the get-go. Gord Schindler

Sounds like the LSN is set too rich and causing her to load up at idle. Is the transition from idle to mid-throttle slow and smoky or crisp and powerful? Also, if you're running a cold or medium-cold plug switiching to a slightly hotter plug will help keep her lit until you get the LSN set correctly.
Doc

I have an OS 46AX on my H9 Ultra Stick 40. I have run at least 50 gallons of fuel through it without a bit of trouble. Also when I fly, I wring the living Hell out of it.
Max engines don't require an extensive break in period. In fact, they fly fine right out of the box. For mine, I used the abbreviated break in recommended in the manual. After that, I tweaked the high speed mixture over the next half dozen or so flights. Since then, I haven't touched it, and I never touch the low-intermediate speed mixture!
I recommend no more than 5% nitro with some castor as part of the lubricant. I mix my own fuel, since I use so much of it. You can buy methanol, castor oil, synthetic lubricant, and nitro at most go cart shops.
Frankly, I doubt that your problem is the engine. Start tuning from scratch according to the OS manual. Don't touch the mixture valve. If you can't get things right, you should concentrate on your fuel delivery system:
1. Can you easily pump the fuel into and out of the tank without problems? If you can't, you have a pinched line.
2. Are your fuel lines intact? Examine them for holes. In fact, throw them away and replace them.
3. Is the clunk still atttached to the internal tank line? Better yet, replace the line with a new one. Is the clunk free to move around in the tank?
4. Is the fuel tank at the appropriate level for the engine? You OS manual gives guidance.
5. Replace your glow plug.
6. Check your muffler to ensure it isn't leaking. A good idea is to make sure the long bolt that holds it together is tight. Also let some CA leak into the threads, so you won't lose it.
All Max engines including the AX have a reliable idle; however, you'll have to clear the carb from time-to-time if you let it idle for long periods. I have never had a Max dead stick on me unless the tank was empty. You should know through experimentation about how much flight time you have with a full tank and then use a kitchen timer or your computer radio.
Ciao,
Mr Akimoto

Excellent advice that I forgot to mention. We all tend to go for the engine rather than look at the fuel supply.

On every modern OS I have seen that is not an air bleed design, pressing in on the rotor (as while adjusting the idle screw) causes significant leaning of the mixture. For that reason, there is a spring that pushes the rotor outward to take up the slack. One problem can occur if the throttle linkage pushes the rotor inward; the result is an unstable idle mixture. A 46FX I have seems to have about .04 slop. However, that will have no effect since the spring takes out all of the slack.
For what it is worth - - - -- Mike Norton

Could it be that the spring got left out at the factory? Things like that do happen. Very easy to check. If the rotor pops back out after pushing in on it, it probably has the spring.

Try an Enya #3 plug.