Is it for sure the Catalytic Converter?

I have had an issue with my 95 Jetta that is quite honestly driving me
crazy. I will give you as much history as possible and god bless anyone
that can really help me.

I bought the car a few years ago. It ran fine when I bought it. When it
is started, about 20 or so minutes in I will see the engine light come
on. It has done this since day one. Gradually over time I have noticed
that the car runs fine when the light is off but as soon as that light
comes in the performance goes down the tubes. It bogs down heavily and
sort of sputters. However once that light goes back off the performance
returns right back to fine.

So I take the car into the dealer and they tell me that it is a timing
issue and they will look into it. THey call me up and say the timing
belt needs to be replaced. I did argue with the guy for a bit as the
fix didnt match the issues in my opinion....either way I went ahead and
got the belt replaced. I get my car back...same thing. 4 visits and
$600 later the car is still not working.

The car is in a state now that the light is on 80% of the time and it
dies now. From time to time it will snuff out completely when I go to
push on the pedal. However as soon as I stop the car it will run fine
again.

SO I have been told it is the catalytic converter....and from any posts
I have looked at that address issues with catalytic converter on this
car on this year the issue match almost to the T.

What does anyone who knows more than me about this car (which will be
almost all of you) have any insight on this?

Things to note: It has a brand new rotor, cap, plugs, plug wires, and
fuel pump. The timing is correct and as far as I know, the distributor
does not need to be replaced...even though the dealership mentioned
that as a fix...but after the assistance I have got from them I am
going to take my chances on the net.