There was a combination of things. Sketchup released a new version, and 3D Connexion released some new drivers to go with it, but they caused issues.
3D Conn then released some updated drivers, which appeared to fix the problem, but in fact they were causing the whole computer to slow down in the background.
slbaumgartner introduced me to the Activity Monitor, where I could see that whenever the 3D mouse drivers were engaged, they started using memory uncontrollably, and within a few minutes of initiation, the whole computer would lock up.
I jumped through hoops of fire (along with a bunch of others with a similar problem) trying to remove the drivers and re-load them (learning along the way that the location of the drivers was in an Application Library on the HD, not under the user name as everyone thought at first).
About 20 attempts and restarts later, and having tried every convolution under the sun, I eventually found that the only reliable solution was to disable the drivers and disconnect the 3D mouse.
Ever since, I have been trying to find a decent solution, with no success.
The best I ever got out of 3D Connexion was for them to tell me that there was a new driver available, but when they told me the version number of the new driver, I realised that I already had that one.