I have some video hardware experience, but I must admit I am stumped... If the same monitor and cable give good results with C64, I don't know why C128 would fade away (especially after replacing capacitors).
The only thing I can imagine is that C128 has a bad power supply, and/or your cable/monitor is drawing too much power...
Imagine: C64 has "superb" power supply and your monitor/cable is "defective". The defective monitor/cable is trying to "drain" your computer, but your C64 has a "superb" power supply so it "wins" the battle.
Imagine: C128 has "average" power supply and your monitor/cable is "defective". The defective monitor/cable is trying to "drain" your computer, and eventually (after a few seconds) your C128 "looses" the battle (picture fades).
--- OR --- Imagine: C128 has "defective" power supply and your monitor/cable is "normal". Your C128 starts with "fresh" colors, but after it "warms up" (a few seconds) the drain from internal C128 parts increases, which reduces output power (because power supply is defective).
I have no way to prove any of this, but it is the only logical thing I can imagine based on your description and my engineering experience.
In summary, try another power-brick for C128 (my best advice). I hope you find a solution (any solution, not just mine) and tell us all about it ...
For you, only Lumafix helped... Can you explain Lumafix for me? (I've never heard of it)
The unintentional vertical stripes in the video output is caused by other signals leaking into the video output. Lumafix is a small board that is placed under the VIC chip to add a negated version of those signals to get a more clear picture without stripes.