Since you have no problems when the trans is cold, and it sometimes engages when you rev the engine a little, then fluid pressure is what is making a difference.
Did a little search and found something that is quite likely to be causing your problem, the fluid filter in the pan may be clogged up which would give the above pressure problems. Check out the second and third paragraph of this link.
http://www.se-r.net/transaxle_clutch/auto_lsd_info.html
Please post your findings if you solve the problem for the benefit of others.
