electrical ceiling box keep breaking

It may be more than the box failing. If you have a fan, the box may not be correctly supported or you may have vibration in your fan. I had those blue plastic boxes on every ceiling fixture and were starting to fail. We updated the fans, etc and I changed them out to the deep metal boxes and supported the box with a 2x6 between the joists. Problem solved. As to calling someone, I don't know your skill level but if you are uncomfortable with electricity, definitely call an electrician.

post a pic of the electrical box

Not much help without a pic of the actual box. Are the plastic holes stripped out and the screws don't grab or the plastic holes broke off the box. If the holes are stripped you could fill them w JB Weld then drill a new hole after the JB Weld cures.

If the tabs with the screw holes are broken. Replace the box w an old work box. The one in your pic is a new work box.

New work boxes (nail-on) attach directly to studs/joists before drywall for new construction, featuring built-in nails/screws; Old work boxes (remodel/retrofit) install into existing drywall with adjustable wings or clamps that grip the drywall when screws are tightened, ideal for adding fixtures to finished ceilings without accessing studs

Had this issue in a house once. The contractor had used drywall screws that were to long and wider then the correct screws intended for these boxes and the box ears were cracked during initial install. Took several years but had several light fixtures fall down and only hanging by the wires.

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The contractor had used drywall screws that were to long and wider then the correct screws intended for these boxes and the box ears were cracked during initial install

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that's 100% what happened

I had this exact same problem recently. Tried glueing the old parts that broke off several times and finally gave up. The box I was dealing with that broke was exactly like the one in your picture and the one I replaced it with was exactly like the ‘old work’ circular box a few posts below yours.

Before you start, turn off the power and disconnect the light fixture from the wires (probably wire nuts). My box was brittle (that’s why the screw holes broke) and I was able to actually just break apart the broken box with my hands by force. If that hadn’t been possible I would have tried with linesman cutters, tin snips or an oscillating saw just to get the old box removed without taking down drywall. If you can get to the nails themselves you can cut them off at the 2x4 with a hacksaw blade in a sawzall, I’ve done this many times with an existing wall box but never with a ceiling box so your mileage may vary in this application as I’m not sure if it’s doable here without damaging drywall. Take care to not damage the wires while doing this. Once the box is broken up, pull it all down and slide the wires from it. Thread them through the holes in the back of the new ‘old work’ box with the paddle attachments on the screws and push that box into place. Screw the three screws (use a drill) in on that new ‘old work’ box until the paddles grab the back of the drywall and reinstall the light fixture.