Over the last few months, since I started this post, my FVP4000T box has gone through a lot of different phases. Currently (touch wood) the box is relatively well behaved but still not quite right.
The box seems to do software updates in the background. Whilst I can't prove it, it often seems to do so in the middle of watching TV: the screen will blank, the box will part boot, blank again, then reboot, then go off - usually at the most inopportune moment of a program! If I turn the box back on, it behaves itself as normal for a few weeks.
Since my last post, I haven't moved the box or made any changes to my wireless networking but its gone from establishing an internet connection every 10 or so attempts, through a phase where it would connect one in 50 or more attempts. A few weeks ago, it was much improved but has started to flash up a new "network disconnected" message onscreen in the middle of programs, temporarily dimming the background picture, then almost immediately afterwards dong the same but with a "network connected" message.
Now (for the last few weeks at least) its relatively stable and the box is either connected to the Internet when I try it, or after going into the network status window and clicking retry once or twice.
Once the box does understand that it is connected, it merrily streams several hours of catchup TV without issue.
So, whatever software has changed within the box seems to have been for the better, though I wouldn't go as far as to say the problem is fixed.