I called in to my local Honda Agent this morning in case it was a well known problem, with a fix...but not the case. He did say they had a lot of problems with the CRV initially because the system was too sensitive. He also said a lot of people didn't realise the calibration requires 30 minutes of driving.
My current take on this issue is that tyre pressures will drift very slightly over a few months and so it is not surprising that the system could trigger after a few months. Not that it will, but not surprising that it does.
The system is quite sensitive so if maybe one of my tyres was actually 0.3 psi over spec when calibrated and drifted down to 0.3 psi under, I might still measure it and say the pressure was OK. 0.3 psi is probably within measurement accuracy of an analogue gauge. But a change of 0.6 psi might well be enough to trigger an alert.
Regular pressure checks and reinitialising should therefore prevent false warnings. I will start doing mine every month or so, when I know I am about to drive at least 30 mins.
I can only explain the double events that Deeps and I experienced yesterday, by surmising that the first calibration was unsuccessful, which is why both of us had the second warning 30 mins after the first. In my case I had to do the first calibration with hot tyres, reading 36 front and 35 rear, since I had to pull off the motorway to do it. This might contribute to why the calibration failed. I did the second initialisation just before setting off home after the car had been standing in the shade for 3 hours, and pressures were 33/32.