Shifting Issue

I have an 87 LX 5 speed notch that I have had since new. It has 54K original miles, and still has the original clutch, quadrant and T5 with the only change being a Hurst shifter that was added may years ago and I am trying to figure out this issue. It will shift great , no noises etc then suddenly be very difficult/impossible to put into any gear. If I shut the car off then immediatly restart it it will shift fine again. I have driven the car for hours before this happens BUT also driven it for 5 min and had it happen. Any ideas as to what is going on?

Thanks to everyone and yes it does have the stock cable and quadrant in it. Just drove it for a half hour and it worked fine but the issue I described happen twice while driving it last weekend. I have tried the foot under the pedal adjustment before but have never heard a click of any kind. Could the self adjust mechinism be bad? I will probably try putting in a new cable though at 54k miles I did not think that cable stretch would be a problem and see what happens.