The reason I believe we don't have the "keep me signed in" is for security reasons. TubeBuddy tool requires authorization and signing in using your YouTube/Google account, to make sure that such authorization is being granted by the users themselves, when they enter the passwords manually, it makes sure that you're the one who is trying to login to your account to access your YouTube details, in this case, trying to access your TubeBuddy account for your YouTube channel.
I don't believe we might be having any changes coming to this in nearby future, however, If there are any such changes that are planned, we will keep our users notify so that they're aware of it, however, our users' security is more important than anything so this might be tricky.
Although I do believe that If you've logged in for a few seconds and have just logged out, you do get a chance to directly skip the log-in procedure of entering your google details, you just have to then click on "My Account". I haven't checked for how long this works, but I'd say for at least a few minutes until the system automatically logs you out.
I am not sure, as this OAuth stuff can get really confusing really quick... but I believe this is likely a setting in your Google account. It's not TubeBuddy that is requiring the constant sign-ins. TB simply requires OAuth to sign in, what happens after that is up to Google.