Gas and Oil Home Heating Furnaces - Furnace Ignition Problem

Hi. I have a Carrier 58DRCO65121JB (I think that's the model number) gas furnace. We have had a problem for a while -- it will run fine for 1-3 days, then will fail to come on. We have been able to "jumpstart" it by turning off the heat on the Tstat and then turning it back on. A few days ago a repairman came and tried fixing the problem. He said it was the ignitor and replaced it. His reasoning was that he heard the ignitor click multiple times and this would cause some safety switch (24 volt?) to turn off the system...by turn off the heat on the TStat he said that we were resetting the furnace. Anyway, the problem is that now we are having even more problems than before. It has gone off multiple times and even when I try to reset it now, it seems as though the ignitor just keeps clicking away and the furnace does not fire up. I know nothing about furnaces and don't want to throw a bunch of $ down the drain with someone who can't diagnose the problem. Can someone please give me some ideas? Thank you very much! Julia