I think I found the problem about why my delta-V vanished! And that's not about the glitchy orbit apparently. I tried to burn retrograde at the perihelion with only my final stage, which allowed to spend 6246 m/s in a few minutes, and my speed at periapsis diminished from the expected value.
However I think I've discovered a new bug: transferring fuel while the ion engines are burning reduce their performance.
Here is a proof with this ship:
By burning the content of a single fuel tank, the expected delta-V is 3178 m/s. Here, both fuel tanks are at 50% because now ion engines consume fuel from all tanks, the same as RCS do. I'm at 3148 m/s here because I only know approximately when I am at 50%.
But if I redo the flight by transfering the fuel from one tank to the other:
I tried twice, by transfering upwards and downwards, but the result is the same: 2530 m/s. The performance has been reduced by 20% just because I transferred some fuel!
That's good to know
Horus Lupercal don't transfer fuel while you use ion engines!