Reward flight availability.. mystery to me !

I'm travelling Upper Class, LHR to NWR in January and returning about a week later via LAX.
I've got enough miles so the wife can accompany me in UC but availability on the VS1 flight is zero at the moment (VS8 return leg is ok).
I assume 'miles' seats are initially allocated and reviewed depending upon sale of revenue seats. Does anybody know what sort of timing is worked to e.g. is the status reviewed say once a week and seats made available on Monday.. or what ? Speaking with the very obliging people at the call centre doesn't seem to offer much explanation.
Seems a tad haphazard just blindly ringing on the off chance. Any enlightenment much appreciated. (PS love the acronyms. Just don't understand most of them)
Many thanks in advancejavascriptinsertsmilie('[}:)]')
Evil [):]

as a rule of thumb, don't hold out much hope for a G reward seat on a Thursday,Friday, or Saturday outbound, or Sat, Sun or Mon returning, as if they are not available when you originally want to book, they normally (particularly for New York) only get released within a few days before travel, as those are the most heavily travelled days. Business travellers to NYC tend to book very late, so they always wait to release more miles seats until they are pretty sure that they cannot sell them for 'cash'

Thanks for the quick response. I'm actually travelling out on a Sunday / returning Tuesday. It's not flexible otherwise I'd change it to the similar time JFK flight (which is strangely no problem with availability ?) It's as if the VS1 is massively popular on a Sunday or they haven't released many seats.
I can't work on the premise that there may/may not be a seat at the 11th hour. It's difficult escaping when you've got kids !
Thanks anyway. Any more thoughts welcome.