Solved. I use 'wired' to access a secure intranet, and 'wireless' for general internet use in the office and elsewhere. The wireless connection kept disappearing after I had used the wired connection. Here's a typical scenario:
* Boot up with wireless only - no problem.
* Plug in wired network cable - it takes over and wireless is turned off, at a deep level.
* Unplug wired network cable - no connections! The wireless network does not resume.
* Run the Windows network trouibleshooter to discover "wireless capability is turned off".
* Pressing Function F9 and clicking the Master and Individual on-off buttons does not help.
* Windows network trouibleshooter offers to fix it: accept the offer, and it works again.
There has been a lot of discussion about wireless connections on various models of ThinkPad and numerous solutions offered and I've tried most of them. Finally I got to uninstall ThinkVantage Access Connections and now everything works as expected. In fact it is possible to have both networks active at the same time (for example in different browsers).
Conclusion: Wired and wireless don't mix well in ThinkVantage Access Connections, so just uninstall it.