Not all toilets will flush the first time. People are spending over $300.00 on toilets that won't flush the first time. Users are having to learn to use plungers and it's gross.
The 1.6 gallon per flush toilets have different designs to get them to work. Some of the major name brands have still not gotten their design down. While we plumbers do not agree nationally on all toilets we do all seem to agree that the Toto's always flush and are continuing to make improvements.
It may not be the design. Look in the tank and see if the water level is high enough and how long the flapper stays up. If you hold the flapper up and it flushes is another indicator. Bowl waxes with the plastic inserts will hold toilet paper on occasion resulting in sometimes it flushes and sometimes it doesn't.
This can be a complicated problem solving area. Not all plumbers are solving the same as techniques and understandings are still being developed.
I would check inside your tank first and then check government and consumer reports on what toilets flush to see if yours ever will.
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