"Could PHP do this?"
No. PHP is a server-side technolgy. It knows not and care not what your browser is, or what it does, as long as the browser will accept the HTML output PHP generates. Once PHP sends the output, that's it... end of story.
To due what you're talking about requires client-side stuff like JavaScript or ActiveX. I'd hazard a guess that sap.com is using either ActiveX or client-side ASP since all their extensions are .asp.
I'd also hazard a guess that they aren't actually maintaining a connection, remember that by definition HTTP is a connectionless protocol and server-side scripting languages using HTTP. Rather loading client-side code on your browser which is making it appear as if a connection is maintained. The client side is then given hooks into the site's backend to execute any processing which must occur when event-signal x is emitted.
Besides, SAP.com is a pretty big and heavily hit site. Can you imagine the server overhead which you'd need to maintain an open connection for every single browser window connecting to their site? Ouch!!🙂
-geoff
PS. A cautionary note that I always feel compelled to add to posts talking about using client-side tech. in this way. Client-side is great, when used tastefully it can add lots of functionality and visual appeal to sites. It should never be used to initiate, manipulate, control, or execute application critical processes. Doing this puts total control over your application's function in the hands of Joe User and allows him to disable or truncate your application through his browser settings. This is a Bad Thing (TM).