You ever hear of this trick?
Insert cart into NES as close to the front of the system as possible.
I usually do the above at the same time as pushing down to make sure it just clears the front of the machine. I clean my machine as often as possible to stay clean. I still have an original working NES.
As you probably know the contacts on those 72-pin become bent from inserting the carts which leads to the contacts not lining up.
The other thing I sometimes do is clean off the contacts on the carts themselves. These can become rusted. An eraser is good for this.