Have you checked your intank fuel filter? A friend had same thing happen ended up being fuel pump and filter..

 

I had a similar problem on my 05 softail. It would stumble and sputter occasionally when at cruising speed and would back fire real bad on deceleration. Start every time and idle just fine and only did it every few minutes.

My dealer diagnosed it right away and repalced the fuel regulator to fix the problem.

Hope this helps.

 

Temp sensor in the front head.

 

My '99 SuperGlide was doing this VERY thing....but now, runs like a top.

I had gotten caught in a rainstorm...ok, freakin downpour from hell the last ride. Got home, put her away.

On the next day out, she was doing the same thing you are describing...hard accel, no problem, low speed, no problem, crusing....jumping and jerking like crazy.

I did the same, drained the gas, tried again...still doing it. On a whim, I added some StaBil to the tank....it has a carb cleaner and water remover in it. Now she runs smooth.

My thoughts are even though I drained the tank and put in new gas, that I had water in the carb bowl....after the StaBil, it is like it never happened.

Don't know if that will work for you...but it sure worked for me....grand total cost of less than $5...

 

If your bike is fuel injected (You say its a 1996???) you may want to look into this...

I have an '08 RKC. I was experiencing the same sputtering and stalling during cruising speeds to the point that I was scared to ride it more than a couple blocks from home. I took it in to the local stealer but it wasn't dropping any error codes so they were convinced it was my EFI programmer I had installed. I was convinced it was fuel related, not electrical but I ordered a replacement programmer for them to test with. It turns out it wasn't the programmer and.... Aw forget it - to make a long story short, after MUCH encouraging on my part they narrowed it down to a plugged injector.

Shortly after getting the bike home from the stealer I was installing lots of parts on the bike (bars, cables, etc.) which required me to remove the tank a few times. One of the times removing the fuel line from the tank I saw what appeared to be a small piece of rubber hanging out of the tank fitting. The tank fitting is after the fuel filter so I assume something in the assembly process caused the rubber piece to be left in the line. At some point it appears a piece of the rubber worked it's way down to lodge in the fuel injector.

I put another 10K miles on since then and all is well.

 

I had the same issue with a used 03 Sportster. The Carburetor Needle was too big and would dump out too much fuel-flooding.