Verry Strange. Never seen that happen in my 35 yrs of working on them. Usually when they have a short in happens right when they start.
It is possible one of your elements is broken or after the furnace gets very hot and expands, one of them is touching bare metal and shorting. There are porcelain insulators inside the duct part that hold them and maybe one is cracked. Or you got some burnt shorting wiring. May need a electrician or heating Pro familiar with elec furnaces to check it.