Cycle frame paint.

Spray.bike fan here. Semi mat finish, so not the deep shiny lustre of a pro job, but much better than any rattle can job I’ve done with cellulose or other paint. 

Best part is it doesn’t run and drip round fittings.

Hard wearing too - this is our kids CX bike and it is standing up to the abuse of a cross season well.

Take a look at spray.bike paints, made to make DIY more successful.

You need to start with a primer specific to the metal you're painting (I've found an etch-primer is best). This is the most important part as it bonds the paint to the frame. You then need enamel paint (enamel is a harder paint that chips less readily and is readily found in spray cans). A couple of layers of clear coat provide protection against scratches, surface rubbing, and minor chips. If your paint isn't bonded to the frame properly it doesn't matter how tough your top coats are, they will chip.

Process:

Sand back paint to remove all chips / imperfections, rust. For best results strip / sandblast frame. Be very wary of sandblasting. On both alloy and steel frames the metal may be only .3 - .4mm thick in places and vigorous sand blasting can actually go through, or seriously weaken the frame -personal experience

Wipe frame down as recommended on primer instructions

Primer coat

Sand lightly to remove lumps, bumps and dust. Wipe down

2-3 enamel 'top' coats (whatever your paint of choice is, car paints will work best)

Sand lightly (1000 grit) and wipe down between all coats to remove imperfections but mostly to provide a 'key' for the next layer of paint.

1-5 coats of clear coat (personally I think that more than 2 is not really necessar). Sand very lightly between coats. 

I had painted an old steel frame with matte color and laquer top coat with poor results regarding chipping as instead of primer I had just sanded the original paint as some forums suggested.

If I wanted to paint now a metal frame and wanted good results, I would sandblast the frame, apply primer, good paint (maybe this cycle specific https://road.cc/content/review/228960-spraybike-paint ) and then a laquer. But taking the color off would be not that easy so I would take the frame to a car rim paint shop to have sandblasted it there and painted with electrostatic paint.

A clear laquer top coat might help. But sounds like the undercoat hasn’t bonded to the frame properly for some reason. A wipe down with a solvent before painting next time will help remove any last traces of grease before priming.

Or could be the paint is just not tough enough, might need to look at the car spray cans in Halfords as an option. I've had success respraying a frame with those.

However, spray can paint is not as tough as the powdered enamel that is more commonly used on new bikes. But you need a spray booth, airline, mask and oven for that - or find a company that can do it for you.