Gas flow is inconsistent,the flame comes on then goes out and then back on again?

Its mostly the problem with gas pressure regulator, when the regulator fails the gas flame goes erratic.It glows high, then suddenly gets low or goes out completely, then suddenly comes out.The flame does not remain constant when gas pressure regulator gets faulty.------- But many a times dirt gets collected in the burner holes and cause this problem.But in your case you mentioned that all burners show same problem with flame coming and going.So burner holes dirty, is bit rare in your case.-------- As per the problem , it indicates problem with gas pressure regulator.Remove the regulator and clean it and reinsert, if still same problem, then it has to be replaced.

----------------