My wife's 2012 FZ Suzuki Swift Sport's transmission reacts like it's “slipping” from time to time and when going up hills it experiences high revving. Sometimes when in motion, taking the foot off the pedal allows the automatic gears to change when pressure on the accelerator is applied again. It sounds like it's electronic. It has low kilometres for its age and has only seen city/urban driving. Can you confirm what the problem might be and if this is a common problem with the auto/manual gearbox by Suzuki?
While the less sporty versions of Suzuki’s Swift of this era used a conventional automatic transmission, the Swift Sport used a CVT transmission. And I’m wondering if maybe that’s all there is to your question. The CVT is quite capable of feeling like its slipping when you use lots of throttle, such as when going up a hill or accelerating to overtake. It’s actually quite normal and is the method a CVT uses to maximise fuel-economy by keeping the engine operating in its most efficient zone.
But if you’ve owned the car for some time and its behaviour has changed, then it could be that the CVT is beginning to wear internally. Or perhaps it’s the torque-converter (that links the engine to the transmission) that is starting to wear out and allowing the engine to rev harder than it used to for a given road speed.
Suzuki did recall this model (and conventional automatic versions) to check for loose bolts that secured the torque converter to the transmission. But if these became loose and fell out, you’d have no drive at all, so I don’t think that’s the problem here.