Oil furnace reset button tripped occasionally for the past 10 days

I have a 1986 ultra 80 furnace with a Beckett model burner. Since 12/10, we started to notice that sometimes when the "system on" indicator on our thermostat was on, the furnace didn't start. When we checked the furnace, the red safety light was lit. When we hit the reset button, the furnace always started immediately as long as the temperature set on the thermostat was higher than the room temperature it read. Then the furnace stopped on its own when the room temperature reached the set temperature, and could start on its own when the room temperature dropped below the set temperature. This problem doesn't occur everyday, and cannot be reproduced by ourselves. Accordingly to my notes, we experienced the problem on 12/19 (twice), 12/16, 12/15, 12/13, 12/12, 12/11 (twice), 12/10 (twice). The furnace was tuned up and vacuumed by professionals last winter. We also had the transformer replaced last winter to fix the delayed ignition problem that tripped the reset button a few times. We don't think there is delayed ignition problem this time since the furnace can start immediately after we reset it. Initially we suspected the problem might be due to failure to sense flame. On 12/16 we saw the reset button tripped about 45 seconds after the furnace started when we happened to be near the furnace. However, for all the other times, we didn't know when the reset button tripped, and the furnace could keep running after we hit the reset button, not keep tripping within a short period of time. Anyway, we cleaned the cad cell on 12/17 (although it didn't look dirty at all when we removed it from the furnace) and tightened the wiring connections. It didn't have problem yesterday but today I had to reset it twice, first time at 5:15 pm when I tried to increase the set temperature on the thermostat, and second time at 8:50 pm when the thermostat tried to start the furnace to maintain the set temperature. The furnace stopped normally and is not having problem at this moment.