Short burns will kill the unit. MOre description on how it is hooked up might help. The unit is either not installed properly, the zones are too small, or it is way oversized. Now, you'll probably say it's the same size as the old one, but then that means it is probably 3-4x oversized.
The load needs to be bigger to keep it from short-cycling. How you can achieve that will depend on what you have and how it is currently arranged, but if it is truely way oversized, it's tough. You may need to add a buffer tank to create a bigger load.
Most boilers have a min/max setting - yours may be set too close together. Also, you may need to consider an outdoor reset control that will adjust the boiler's temp based on the outside temp (thus load). It's highly likely that for most of the winter, you could heat the house with lower temp water. There's a limit on how low you can go based on the specific boiler or you'd be adding to its early demise. Some can handle low temp returns, some can't and will corrode or the shock will warp or crack them.
As an aside, double check the operating pressure and make sure it is within range.