Yucca problem

I have a large indoor Yucca with multiple trunks bearing several stems each.  The new leaves grow well but then turn brown, curl and dry up and then die.  The lower old leaves are fine.  I've tried treating the plant for insects and fungus but no success.  Does anyone have any idea what this could be? 

Where in the house is it?

Hi, have you over watered your plant or given it to strong feed?I have a yucca which I put out in summer(I don't leave it out in winter as last year I nearly lost it to the severe weather).I water it when its really dry and mist leaves if indoors.I feed only in summer a weak feed.

Just a thought . Have you turned your central heating on ?  Is it near a radiator or in a draft ?