I live in MEL /AUS and I have a DUX tankless hot water system (on-demand gas system). Since two days ago, our upstairs bathroom and downstairs master beddroom do not have hot water--water pressure is good from hot taps but only run cold water (I mean cold, not warm at all! ) But downstairs kitchen and laudry room have great supply of hot water.. I believe the water circulate in my house as from Laudry (the closest to hot water unit outside), to Kitchen, to upstairs and finally to the downstairs master bedroom (this is why master br has no hot water either.. )

We have always been very cautious when taking shower. We turn the hot water on and run for a while then need to be very careful in turning cold on--very slowly bit by bit to adjust the temp. Otherwise the water becomes totally cold (very BAD/SENSITIVE TEMPER)... But normally if we restart the hot water will come back... but this time two days NO HOT WATER AT ALL.. it happened last year and now again.. no one can take a warm shower now.. I checked the unit outside it works fine... can anyone please help? Thanks

You probably have water saver showerheads. My understanding is that water conservation is a huge issue at your end of the globe.
Try taking a showerhead off and see if you get hot water at that fixture. It is possible that the heater isn't seeing enough water passing through to start heating. If you have to be that careful when adjusting temperature it certainly sounds like your heater needs to be serviced.
Good luck!

Assuming you have a single handle or knob shower valve. It probably has a pressure balancing spool to maintain the selected temperature. It has been failing intermittently and has now stuck on the cold side.
Solution is to replace the pressure or temperature balancing mechanism in the valve.

Thanks Chayn and hkstroud for the help. The problem is not only shower has no hot water but basins and tub. And I acutally have double handles for hot and cole separately for every single fixture. When first turned the hot on, there is smal stream of hot water. But a little further try for bigger run turns out cold totally... :(

How old is water heater. Do you have single handle valves any where in the house? Do you have a hot water recirculation line?

Have someone open a hot valve upstairs slightly, while you feel the hot water output pipe on the water heater. It should get warm. Then have them increase the flow, does the pipe get cold?