Assalam o Alaikum.
I have a 2003 Vitz on Petrol locally driven 80k in Khi and now Lahore.
I have very recently experienced the same issue for the past 6 months. Last month, first for the radiator replaced with a good Kabli one from Bilal Ganj, got it serviced before installation, still the water was evaporating and I needed water fillup, although less intensely now.
Then my mechanic suggested to check the Head Gasket, we opened the engine block, first time ever, and yes that was all expired due to excessive overheat.
We got the gasket replaced, head block shaped from a Lethe machine, fine job he did. Some belts, seals and rubber pipes were also changed as I didn't want to make frequent visits to my mechanic in near future 
Alhamdolillah, this past weekend, I made a round trip to my native town in South Punjab 550KM from Lahore on the Vitz. Remarkable performance by the engine, AC and awesome fuel consumption of 16.3 km/L with AC all the way, speeding at av. 100km.
I suggest u get the gasket checked, but also if u get the car scanned for any out of spec settings, may be that would help.
Good luck bro!
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