I have an 88 Festiva that sometimes will not get going after it has stopped and then stalls out and then will go again after an hour (usually). What is the problem?

I have an 88 Festiva (carb). The last two years, for about 10 times, it will act as though the fuel filter is clogged. You give it gas, and there seems to be gas flow, but the car may go a quarter mile in first gear (and it always happens when I have come to a stop) and then finally stall out. If I let it sit for an hour, it will work fine, except for two times when it would not start after trying it three times in two hours and I had to tow it. My mechanic has checked it out, although by the time I get it to him, it works fine. The fuel filter is clean, the carb is good, the fuel pump has good pressure. What could be the prolbem? Tim Williams Sebring, Fl