How Do I Keep Gingerbread Men From Softening Up And Falling Apart After Only A Day On The Tree?

I can remember at school we coated it with clear glue and let it dry after it was complete and hard.

Purplej:  A couple of things you might try.  Increase the flour in the recipe for a stiffer dough.  Of course this will make the gingerbread harder rather than very soft and chewy, but still tasty.   Or...Maybe you could separate the batch of dough before baking, adding a bit of additional flour to the one which you'll use for ornaments, and leave the other batch without added flour to make others you can have soft chewy ones also on hand for the grandchildren.

Alternatively, my mother used to coat the completely cooled gingerbread forms with a very thin glaze made of powdered sugar and milk.  It dries almost clear to opaque.  This seems to fortify the gingerbread.

Also, I don't know if you would consider trying a whole new recipe, but if you are interested, here is a link which gives the recipe for gingerbread used to make gingerbread houses, which is a bit of a stiffer dough.  The recipe says to bake at 190 C, which is the equivalent of 375F.  Here you go and good luck!
Gingerbread recipe

PS - What a great tradition!