It's hard to tell exactly in your case but the fuse will only blow if there's an overload of current that the circuit is not designed for or a short cut to earth.
The fuse melts but does not blow cause its got a loose or a bad dirty connection at the fuse holder for a start. This means the normal operating current for that circuit is finding it harder to get round (for want of a better description) cause of the corrison or dirty connection. This leads to higher resistance which means way more heat in that surrounding area which leads to the melting.
Loose pin holders can cause arcing between the plastic and the holder to I believe, which will melt the plastic to.
Add in the poor quality of the plastic in the fuse box and lots of heat in there already which only adds to to it.
Regularly check and clean your fuse terminals on your block and make sure the terminals fit nice and snug into the reciptcles.
The oxidation is not always obvious.
Also keep the lid off the fuse box holder is another tip I've used
I had to replace one of my melted fuses with a fuse extender and when I took out the pin from underneath I could see oxidation on the copper strands themselves leading to the pin. The copper had turned jet black, not good.
I'm not an electrican so if Im wrong with any of that there, please correct me!
Cheers
Shane