Suzuki Vitara, 100 KW, 2000 cm3, often goes off when switching down, what can it be?

Hello, in the circle of friends a Suzuki Vitara, 100 KW, 2000 cm3, Bj. 1998 is driven. Unfortunately, when switching down e.g. from the 5th to the 4th gear, or from the 4th to the 3rd gear of the often instantaneously simple. So of course also the power steering is switched off, which is already dangerous during city rides. What can it be, do you have some target-oriented tips or hints? Best regards – Willi