The reason I want to install an old kernel is that my laptop WiFi adapter doesn't work well in monitor mode. By that I mean, airodump shows all clients as "not associated" when they actually are.
In the past, I managed to fix that by installing the kernel image 4.0.0-kali-686 pae, which worked well with the wifi driver (b43) for my wifi adapter (BCM4311), but it's been over 3 years now since I last used Linux and I don't remember how to do this.
The "not associated clients" problem has to do with either the wifi driver or with the kernel, but I don't know which one is to blame. I installed the latest version of Kali Linux earlier today and just updated and upgraded it. If it helps, the "not associated" problem was encountered before and after the upgrade.