You wouldn't be able to send me the model because I don't have Comsol, so I couldn't do anything with it. With respect to the RAM issue, I do remember having problems with a demo version of Comsol where problems of a certain mesh density would not solve due to a problem with the solver not being able to use virtual memory, only system RAM. Not sure if this problem has been fixed, but it's something to keep in mind since it is quite possible you are using up your ram depending on how many elements you are working with. You could always try making your mesh coarser to see if the problem converges.
Technically speaking, there aren't any fundamental reasons you can't raise the flux past a value before the solver doesn't converge, it's really a case-by-case thing based on the problem being solved... You mentioned that you were calculating the density of the air using an equation (I'm assuming a temperature-density relationship). I would suggest removing nonlinearities like this for a first attempt. First, try to solve the simplest problem- heating bottom of the plate, constant h-value on the sides and top. After that, you can begin to add degrees of complexity. It's also possible it's better to model a burner as a constant temperature source rather than a uniform flux source, as a flame will have a combustion temperature associated with it...
If during the solve you're getting semi-infinite convective currents, it may mess up the convergence of the solution depending on the solver's settings for determining convergence. If, after adding a level of complexity the solution refuses to converge, you know the culprit and can adjust things accordingly.
Also, you may also consider trying to solve this problem analytically, to see what numbers you should expecting. An iterative process between a steady-state 1-D conduction model and free convection model using resistive-thermal equations should give you a good idea of the average temperature of the plate, as well as convective currents outside of it. It's possible you're barking up the wrong tree and the copper plate will melt before it reaches steady state if you don't take into account radiation effects... Better guesses at the start of the process could yield better results at the end.