Hi there,
It does not seem to be a problem wit the specific code.
e = Classify[{Import["http://www.bbc.co.uk"] -> 1, Import["http://abdn.ac.uk"] -> 2}]
runs without any problems on my machine. Are you using Mathematica Online/Programming Cloud or are you on a Laptop/Desktop? (To figure out whether it might be the connection to the cloud that's causing problems.) Can you open the websites in a bowser or do they time out there, too?
If the import function is repeated a lot, it could be that some pages time out. I programmed random walks on websites and that happened quite e bit. Another thing is that if Classify waits for the websites to download and they take too long, Classify itself times out.
In summary, I guess that we'd need to know more about the problem to be able to help.
Cheers,
Marco