I investigated the issue a little more. Whenever I put the computer into standby mode, I need to unload the tg3 module again. When the module was already unloaded before suspend, then I have to load the module after suspend to get the SD card reader working. So both actions awake the SD card reader: loading the tg3 module as well as unloading the module. Before the BIOS upgrade, I had to load the module, unloading had no effect.
I investigated the issue a little more. Whenever I put the computer into standby mode, I need to unload the tg3 module again. When the module was already unloaded before suspend, then I have to load the module after suspend to get the SD card reader working. So both actions awake the SD card reader: loading the tg3 module as well as unloading the module. Before the BIOS upgrade, I had to load the module, unloading had no effect.