What could cause my boiler to ignite 3 times then goes off?
If you get good ignition and the boiler's ignitor stays on the entire time even after you have flame, then your flame sensor or controller is probably broken.

Otherwise, you have a mixing issue. Either not enough air is being moved by the fan or oil is not flowing sufficiently, possibly because of issues with the nozzle.

The 3 times lockout is a safety feature that keeps the boiler from filling up with unburned oil that possibly ignites in an undesirable way.