There could be several problems.
First, make sure the engine is not running lean at idle. Many folks don't realize that it is harder to get the correct mixture at idle than it is at wide open throttle. One of the side effects of being lean is the engine builds up heat and may not recover when the throttle is opened. A good idle mixture setting is indicated when you can pinch the fuel line and the engine picks up a couple of hundred rpm and then dies after a few more seconds.
Second, if the engine is too rich at idle, fuel pools inside the engine and when the throttle is advanced the engine can't clear the liquid fuel charge in the case and the charge may interfere with the flow of the incoming atomized charge. If this is the problem, when the throttle is wide open the intake sound (you can hear it because the exhaust sound hasn't come up yet) has a kind of "hollow" sound to it. If the mixture is really rich, sometimes pinching the fuel line won't stop the engine for a very long time. It might not even speed up any. The engine can end up with a real rich idle mixture when chasing a low idle speed. Be sure that the idle speed you are looking for is reasonable. The idle speed only needs to be low enough that the model will not maintain level flight, well maybe a little lower so you have a controlled decent. For a 35 size Carrier model (say 2.5 pounds) and 350 sq inches this rpm is around 3500 rpm with a 6" pitch prop. You may find that the idle rpm only needs to be around 5000 rpm on a 15 size model to be flyable.
Basically you have to find a lean idle mixture then work back to a slightly rich mixture setting. Always set the idle before moving to the mid-range (if there is a mid-range adjustment) and then on to the high speed mixture.
Third, many carbs have a lean mid-range. This manifests itself by poor throttle response in the mid range. Various Perry style carbs are known to have this problem. If you remove the idle disk you will notice that there is a round hole with a "v" shape on both sides of the hole. The shape (size) of the "v" sets the mixture at idle and the mid-range. The hole (with the high speed needle) sets the high speed mixture. If the engine is really going lean in the mid-range, opening the "v" slightly will enrichen the mixture. Be careful, a little change here is a lot of mixture change. A couple of spare idle disks is probably a good idea if you want to try filing the "v". By the way, pay attention to the o-ring on the idle mixture disk. If it is bad, nicked, worn, or just plain old it will leak air and cause a lean mixture. A symptom of a bad o-ring is a changing idle mixture even when you don't touch the idle disk.
Good luck,
Dave