How large and sealed of an area are you using it in? I ask because those units have a low oxygen sensor which will shut it down if there is not enough oxygen in the space.(kinda prevents that pesky suffocation thing). Otherwise if using it in larger cold spaces, the issue is can be from the smaller tanks. As mentioned above, a larger tank can solve this, because these units have a fairly good input rate, which will cause the smaller tanks to freeze, and lower the propane temperature and evaporation rate, basically runs out of gas until the tank warms back up.

Is your Mr. Heater the model that uses two small one pound cylinders or you have the choice to hook it up to a single larger tank? if so, you must use the special filter connected to the Mr. Heater and then your hose to tank.
This happened to me and after I hooked up the filter my problem was fixed.
Ron

Mr Heater has an 800 number. They will tell you how to clean the pilot light. I have a buddy and a big buddy. I had this problem with my big buddy also. If they are stored in a dusty area you need to clean the pilot light.

Try just one new cylinder, it will run on just one, to verify a problem with the cylinders. Also it could be the pilot light, sit and watch the pilot light to see if it goes out for some reason. If it does the heater will shutdown automatically, but you already know that.

I have one of these and it works great, but it will go out if there is a light breeze that blows out the pilot light. Is that your problem?