Intermittent timing fault

I have an 05 SXT with under 60,000 miles. The check engine light is on and it has an intermittent timing problem. When it occurs attempting to run at above around 2100 RPM causes severe stumbling. This seems to occur somewhat randomly, but consistently only when operating temperature has been reached.

I had the codes checked and got a P0344 and a P0325, a knock sensor error and a camshaft position sensor error. I assumed the knock sensor error was a result of a faulty CPS , so I replaced the CPS and connector. The problem continues. I don't think it's the timing belt due to the relatively low mileage and I have never heard of a timing belt "getting better" once it was out of proper alignment.

Any suggestions?

Ras,
Your thinking seems correct that the timing belt should not have problems with only 60k miles on it, and it would not self correct. You noted some details that should be looked into. You mention that the problem only shows when it has achieved operating temperature. To me that says there is something associated with the choke/fuel delivery system. Go over every aspect of that to ensure nothing is wrong. When the engine warms, there should be more air coming in (leaner mix). Could this be as simple as a clogged air filter?
Also you mention the sensors. If it is easy enough, check them and clean them if possible. Assuming you got this car used, the previous owner(s) may have added chemicals to the system, which could have damaged/dirtied up components internally.
Hope this helps.

We bought the car with less than 8k miles on it so it's chemical history isn't suspect to me. I will check the intake for a possible air starvation problem. Who knows, maybe there's a mouse nest or something in there. But with a fuel mixture issue I would have expected other error codes, co2 for example.

One "event" only started after the car was driven almost 60 miles on the highway. The most recent after only 10 miles. I stopped at a store for about 15 minutes, and when I started driving again the problem continued for about a half mile. Then it ran fine for about a mile and a half before resuming for the last 2 miles of the trip.

P0344=
Camshaft Position Sensor "A" Circuit Intermittent
P0325=
Knock Sensor 1 Circuit Conditions
I would be looking at the engine wiring harness as both codes indicate a circuit problem. Timing is controlled by the PCM. Components expand and contract due to heat and cold.

I also have an 05 Neon with intermittent problems electrically. First, it was errors involving the Crankshaft position sensor. This forum said to reseat the connector. With that done, now I have a mysterious Check Engine Light (CEL) that will come on and go off without any percieved engine malfunction. Per other articles in this forum and my brother (mechanic for over 20 years), I think I will run some extra grounding wires. It is a cheap fix, and it couldn't hurt, especially since these cars seem to have a problem with ground connections.
Incidentally, is it possible that the faults that were reported in this post are from a bad ground? The logic is this: when things heat up, the metal expands, and may cause the connection to come loose, thereby causing a fault. Then when things cool off, the connection is restored.