Absolutely in agreement with many, and especially Sean's resounding post, about this. I have just come back from the (British) GIrls' Championship at Harlech, where I saw large numbers of 15- and 16-year-old Europeans hit the ball staggeringly well, and (most importantly) enjoy themselves enthusiastically: I don't think that these kids thought they were playing a dying game...
The participant problem is, arguably anyway, not nearly so pronounced at the junior level, but rather at the demographic 25-40, for both sexes, where simple pressures of time and changing work and family patterns have impacted on voluntary organisations of all kind, including golf clubs (and political parties...). Getting non-retirees to serve on committees, let alone take on (say) the club captaincy, is an increasing challenge, certainly here in the UK, and in turn reflects the business expansion of those same institutions, with many clubs expecting a level of input from those same captains that would have been thought inappropriate a generation ago.
A thread about Clubs is important. One of the (many) interesting things about the commentary of Peter Alliss, and perhaps why his such a Marmite voice within sport, is that for him the defining institutions in golf are golf clubs, and (certainly not) entities like professional tours and executive bodies. This differentiates him from about 90% of those working in the contemporary golf broadcast media, with one or two honourable exceptions. The world of golf that he entered in the UK in the 1940s and 1950s was entirely built around Clubs, and famously the Open Championship finished on a Friday afternoon so that professionals could get to their 'proper' jobs and open up their club shops at the weekend and serve the members. Now clearly, there were numerous aspects of that world - with its emphatic social distinction between the membership and the club servants (including the professional) who worked on their behalf - that we would nowadays find pretty unacceptable. At the same time to have such a base in voluntary institutions has always, historically, been a strength of the game, and it's one reason why the UK casualty rate amongst member-owned clubs has been notably lower than amongst commercial or proprietor initiatives. If the Royal Isle of Wight Golf Club, Bembridge, is, along with Bramshot, perhaps the most celebrated golf club casualty in the UK (9 holes on a tiny spit of land, and you can still stay in the old clubhouse) then that tells you something about the strength of the model. So far, anyway...