What do you mean by "log back in"?
Do you mean going to the iCloud website and logging into your iCloud account there?
If so, then that is not how photos work with iCloud. There is no way to access your photos online with iCloud. It is purely a "sync" service for photos. If you turn on Photostream on your devices, then iCloud will sync those photos between your devices. For your iPad, your synced photos will appear in the Photo app. For your MacBook Air, by default, your photos will appear in iPhoto. For your Windows 7 computer. you specify which folder your want your photos to be put in from within the iCloud Control Panel.
If you want the ability to go to a website to see your photos, then you will need to use some other service such as SkyDrive, Google Drive, Dropbox, or one of many photos services such as Photobucket, etc.
Or do you mean that a photo from iPad is not show up on your MBA or Windows 7 laptop even though you have you iPad set to use Photostream with your Camera Roll?
If so, then make sure your have Photostream turned on in the iCloud setting on both your MBA and Windows 7.