It could be the stat, or the flame sensor, or dirty filter.
Although I wouldn't think a limit switch would cycle that fast.
What kind of t-stat do you have ?
Is it round and gold, with needles to indicate the temps.
Or is it a digital read out ?
Normally if it's not detecting a flame and goes off due to that, the unit will lock out after 3 or 4 trys to light.
So it could be doing what the stat is telling it to do.
Short cycling.