I've been told they need the Last of the Summer Wine repeats for the BBC HD channel as there is still a shortage of HD content available for filling that channel's schedules. That's why we're not getting them on BBC One these days.
Of course there are still the older, non-HD episodes, but they're very rarely going to see the light of day on BBC One while the series is still being commissioned, for continuity reasons. In much the same way as only a few (three?) Compo episodes have been repeated on BBC One since the final Bill Owen episodes debuted. I think only Extra Extra, Last Post and Pigeon, and the 1995 NYD episode (can't remember the title at the mo) have been repeated since then.
I don't know when series 31 will air, but I will post on here when I get tipped off.