I wonder if your CDI box has seen better days. My first DT360A simply would not run right when I bought it. I swapped the stator and flywheel from a DT250 which has points and condenser instead of CDI. The bike has run great ever since.

I think the CDI is ok but today, I had my son move the spark plug wire around with a plug attached and grounded and it sparks when it's held outside but in it's natural position it does not! So, I believe the spark plug wire has issues. I do have a new spark plug wire/coil coming so hopefully this will fix my problem...

I have a similar issue on my own DT360A, but I think mine is caused by a combination of a dodgy connection where the HT lead is fixed to the coil, and having a petrol tank with a slightly narrower tunnel than standard, and this sort of pushes the HT lead away from the coil when I fit it. I get no spark with the tank fitted, but as soon as I remove it, the spark reappears. I am using a tank from a MX250, as my original one is a bit too crusty inside.

I am looking into buying a new coil.

I've had my tank off and on so many times, I've probably screwed up my spark system too. I remember when I first got the bike and cleaned the tank, it would start very easily. Kinda wish I had left everything alone but when I found the flywheel cover was full of water and everything was terribly rusty, I too everything apart...