I have Sketchup Pro 8. I just got a new MacAir

I want to be able to use SU Pro 8 on both my existing MacBook Pro and new Mac Air. Every time I want to use
it on the Mac Air the red license request window come up asking for a license. Must I do this
every time I open the program.

As of now, that is the case.

If by “license request window” you mean the welcome dialog (learn, license, template chooser), you can find a checkbox to not “show on startup”.

screenshot the message box then upload here.

are you trying to run sketchup on both computers at the same time? on the same network? you can only use one instance of sketchup pro at any given time.

No. When I take Air Book to different location, the red temporary license screen comes up instead of the
blue licensed version. It says the server is down and to try later (which makes no sense)

Then I put in my username, password and key and it turns blue and starts working…but it is asking
me to do this every time I open the program on that computer

Traditionally, the license details you input will not stick if you are not using an administrator account to run Sketchup when you do that. Otherwise, SU should run fine with a normal user account.