Funny contacts behaviour

I have just turned on my central heating, and each year it becomes more and more difficult.

It is a relatively old (1996) natural gas boiler, but it is from a good maker, good quality, and it is efficient, safe and reliable.
However, restarting it at the end of autumn becomes more and more difficult, and I have decided to investigate.

The problem is that the gas pilot doesn't hold: as soon as I release the starting knob, the flame goes away, even if I keep pushing it for tens of seconds.
This boiler has an originality: the safety loop is completely autonomous and independent from the rest; it has no external supply.
The safety thermocouple is not directly connected to the gas inlet control, but it is daisy-chained with various safety switches before: overtemperature, overpressure, etc.
The voltage delivered by the thermocouple is tiny: in the 10 to 20mV range, thus any drop along the safety loop would cause problems.

I first thought that the switches were the culprits, but they only drop 1 or 2mV. I then checked the wiring, and discovered significant drops: up to 6~7mV.
The cables themselves cannot be the cause: they are good 1mm² copper, and they have always been in a clean and dry environment.
The connectors are Faston type, regular 6.35mm and the smaller size. When I measure the drop between the male spade and the metal of the female receptacle, I only see a negligible, sub-mV drop, thus the only remaining possibility is the contact between the cable and the receptacle. They are professionally crimped, and look in good condition, yet there is a drop of several mV. I have always been taught that properly crimped connections are airtight and very reliable, but it seems that exceptions exist.
The same kind of issue could affect speaker connections for example, and cause tiny sound degradations: I didn't verify it, but I imagine that this contact resistance is non-linear too, and could add some distortion
I have often seen similar issues in automotive, cables with crimped lugs that show remarkable high resistance between the cable and the lug. Also on cables in the interior. Over a volt voltage drop at currents of just a few amps. And indeed very non linear behaviour.
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I remember those old push to light pilot boilers. My current oil boiler has too much electronics for its purpose so each year spits a sensor. Last year was the flow sensor, this year was a thermocouple so I got heating but no hot water. Luckily parts are all the same no so easy to fix.

crimps should be gas tight, but corrosion is your enemy. My friends with offroad vehicles always dip the bare wire into petroleum jelly before crimping which seals out most of the grot.
Depending on the type, 10 to 20mV seems quite low.
That's the norm for these kind of devices. They are generally directly connected to the electromagnet releasing the valve, but here they they go through a number of intermediate steps instead, which is not a problem as long as each link is ~perfectly dropless.
I didn't make any measurement, but I think that the operating current must be substantial, like hundreds of mA: the loop resistance is undistinguishable from a short when measured with a standard 2k points multimeter (resolution 0.1 ohm) .
In this particular case, there is no risk of contamination of any sort, and the crimping is ribbed, to improve the contact, yet it failed (for this particular application, at higher voltages a few mV are irrelevant)
Yes, and no in my case: the boiler sits inside my house, thus any "parasitic" heat is recuperated, and anyway, the circulation pump operates as long as the pilot light works, thus nothing is wasted. That includes the electrical power for the pump, although it is less advantageous because electrical energy is costlier than gas.