Did it used to work before?
I find that CarPlay aggressively tries to hold onto the WiFi connection and so it causes an issue with most any WiFi related apps/tasks. I also sometimes have issues moving out of my car and switching to AirPods to continue listening to a podcast or something.
To be fair, I've got an aftermarket wireless CarPlay dongle that plugs into my car's USB port and so I don't know if it's CarPlay related or something specific with that dongle. For that reason I often have to physically unplug the dongle to ensure that I get access to WiFi on my phone. (I've done it so much that I've broken one of the two USB ports in my car and it's a very expensive repair unfortunately.)
Do you have other WiFi apps that work fine even when using a native wireless CarPlay solution? or is it limited to Thinkware's app for you and just with the latest version of the app?
I'm working on a video now from Thinkware at SEMA and they're adding Bluetooth to many of their newer models specifically to help with this. Because Apple CarPlay / Android Auto does conflict with connecting over WiFi, connecting over BT allows you to do some basic settings adjustments without having to rely on WiFi at all. Higher bandwidth stuff though still requires WiFi of course.