Here are 3 of my 4 P6139A scope probes. These are all about 14 years old, and for most of that time they have been plugged into a TDS540 scope. No interesting chemicals in the area. All have various levels of crumbling and cracks. Merely touching the white plastic makes it crumble, with a consistency reminiscent of chalk. This seems to only apply to the thin cylinder of the plastic, the remainder seems to not be ready to fall apart.  As can be seen on the center example, all the insulator has fallen out, the one on the right is partially damaged, and the one on the left has cracks in it but I have been very careful not to touch it.
Here is the middle BNC from the above picture after dissasembly.
Here is the insulator from the BNC on the right in the first picture
With a lot of careful measurements, this is what I think the insulator dimensions should be. This was about 2 hours work.
Here are the dimensions for the external diameters from left to right for the X axis: 0.165, 0.035, 0.120, 0.162, 0.268 and the respective diameters are 0.272, 0.327, 0.288, 0.270,0.255
The internal diameters from left to right are: 0.400, .060 (implied), 0.255 and the respective diameters are 0.120, 0.052, 0.201
Procedure:
From the right end drill with #55 0.500, do not drill the 0.201 till later. Do all outside surfaces. Now drill 0.201 with #7 drill. Touch the end of the drill to the end of the work, and enter 0.280
Part off and with a little force, the 0.255 end should fit in a 0.250 collet. Center drill and drill 0.120 with #31 total depth including drill tip 0.400
With a few hours of work I had 4 blank pieces of Teflon ready. A .5 inch stub at one end will go into the lathe collet, and the rest is turned down to .4 inch diameter. My first attempt at making a replacement failed, and the resulting scrap are the two pieces on the right. 3 more to go with a bit more care.
First, drill a hole .052 diameter into the piece. This is the clearance for the center pin, and will also be used for support from the tailstock through the rest of the opperations (what I failed to do on my first attempt)
Checking setup to make sure the cutting tool is at exactly the right height. Then do the first cut brings it down to .327 inch, which is the outer diameter of the thin (.035) triagular wedge (collar) that seats against the compensation box threaded section (see second picture above). Haven't screwed up yet.
Second cut (.288) is one of three diameters for the part of the insulator that goes into the BNC housing.
Third and fourth cut finish the outer surface for the section that goes into the BNC housing.
Now I am cutting the section that goes into the threaded part of the compensation box. Then the diagonal cut on the collar on the side that faces the BNC housing.

Next, carefully drill the large hole for the BNC end, then separate the part from the stub, and drill the compensation box end. This is the point where I broke my first attempt.

Here is a view of the new part and the old damaged part
This is looking into the BNC end
A side view of the finished part
This is the compensation box end of the insulator. The middle pin of the BNC plug only touches the Teflon for a short distance at the narrow neck inside the insulator
Installed the new part. What luck, it fits perfectly.
All assembled and ready for use again.