Why does my boiler keep shutting down and reigniting after a minute?
I feel your pain, been there myself. This could be a problem with your boiler, it could be your system is gunked up, or it could be your thermostat commanding the heating system to turn on and off. My money would be the boiler and not the thermostat, but you could take the communication wires out of the thermostat and twist them together for awhile to see if your boiler stays on. If it does then buy a new thermostat and count yourself enormously lucky that it was that simple and cheap. 

It could be that your heating system needs a flush, which is something you could do yourself with basic tools and some hose. Generally you would flush the system with water, then refill and add a cleaning compound for a couple of weeks, and then flush again and refill being sure to add a conditioner. If you live in the UK then these instructions may work for you. If you're not sure what you're doing then get a professional. 

If it is your boiler and not your thermostat then your best option is to get in a very good heating engineer who really knows your boiler type well. There are simply too many boiler types and things that could be going wrong to give you advice, and you probably wouldn't be able to fix it on your own anyway.