Really? I've kept my VPN on in an active profile while using another and have never seen any evidence that the VPN had disconnected. How did you determine the VPN disconnected?
I've had other profiles active as long as overnight and still received all of my notifications, meaning the VPN had to have been active the whole time. I use ProtonVPN, btw, but I've also used Mullvad and it remained connected as well. I regularly keep my "personal" profile active while using other profiles for games and such, sometimes connected to other VPNs or using the same VPN provider, but a separate connection.
Based on my experience, this isn't expected behavior. Maybe others have better ideas/suggestions. I'll admit my ideas are all farfetched for different reasons, but I'll suggest them anyway.
First, you're sure you didn't end the profile's session? Like you log in to the VPN profile, then switch to the other profile? Based on your description, this probably isn't the cause since you say it takes some amount of time and mentioned battery consumption before you see evidence that the VPN has disconnected.
Second, are you sure the VPN you're connecting to doesn't have time or connection limits? Maybe the VPN server terminates the connection on you if you connect again in another profile. Like Mullvad limits accounts to 5 devices. Possibly you've used up your allotted connections and end up being kicked from the server? Honestly, I wouldn't expect this to be the reason unless you're testing a free VPN.
Third, maybe the VPN app you're using has some kind of issue. Maybe the app is trying to switch servers for a faster server and fails or has a poorly designed internet kill switch? If the app does have an internet kill switch (unlikely), that can be safely turned off since the OS does that automatically. To test if the app is what's causing the issue, maybe you can try using the Wireguard or OpenVPN official apps temporarily to connect to your VPN provider instead to see if you continue to experience this issue.