My SHT31 sensors do not work properly with multiplexer

I've been having an issue with using multiple SHT31 sensors with a Mega Arduino. It turns out that Arduino stops working at some point quite randomly and this took my a lot of time so far. I have several SHT31 sensors connected to a multiplexer breakout board, since the Mega has only one SDA and SCL pins. I turned out that during the process these sensors tend to change the address (probably one of these data connections jumps to VCC and it causes an interruption for multiplexer in the long run). I've been trying to solve this issue, but for the time being my setup is running with only one sensor (without the multiplexer) and there has been no sign of this issue so far. Anyone know how can we make these sensor compatible with multiplexer?