That's an old furnace and anything original will have wear and looseness, etc... .
You'll have to physically remove, bypass, etc,, until you find what is gradually heating up with higher amps.
Completely remove the block, check those lugs carefully.
Just one of them things that takes elimination and will probably be something you think is ok.
Check the fuse holder prongs, anything that can be loose or corroded to associate small ammount of heat to build up over a week or so.
Disconnect one element at a time to see if it still blows. If it does it with each one disconnected at a time, that rules out all but wires and the fuse block.
Some people are Humbly Grateful, while some are Grumbly Hateful.................... Which one are you ?