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The problem is that the location of the tap is nearly imposssible to
access because it's right above a door frame.
Therefore the pipe cannot be cut or welded to replace the tapped segment.
Also the pipe cannot be easily removed because it's about 24' long and
safe access to one end is also impossible without destroying a wall.

What are my options to fix the leak ?

It can be cut, it can be soldered. You just have to know how to do it. A
plumber can do it as they run across tough situations all the time. It may
have to be shielded when the torch is used, it may have to be slowly cut
with a small saw. That is why a pro can charge a decent price. $125 just
to knock on the door is about average.

Installing a new saddle valve may cure the problem if the seal is gone.