Greetings hatchethead,
While I don't have any specific experience with banjo burners, I might be able to offer some advise.
1) what color is your flame? It should be a nice crisp blue with no yellow at all. If there is any yellow, the flame is too rich and is starving for oxygen. In which case, open the combustion air inlet on the burner slowly while watching the flame to achieve the crisp blue flame.
2) is the flame lifting off the burner at all? If it is, this is an indication that there is too much air. In which case, close the combustion air inlet on the burner slowly to get the flame to settle down.
3) if the flame is flickering, it's most likely due to a lack of fuel - low pressure. This issue can be corrected by either increasing the capacity of the regulator or (and this should not be attempted unless there is no other option) drill a larger orifice opening. The oriface is typically brass and it's the hole in the inlet of the burner just down stream of the hose connection. That said, a burner will typically require between 4-8" (depending on the burner) of water column pressure to operate and your regulator may not be capable of feeding that amount. So, that begs the question: did the regulator come with the burner and we're they bought new from a dealer, or were they're bought privatly? If bought by a vendor, I recommend contacting the vendor.
Final item to check is the valve and connection on the fuel tank. Perhaps try another tank to see if the problem persists.
Hope this helps!
Good luck!