With a 10-20 second flame out it probably means it's going over-temp and the safety is tripping.
How many BTU/hr or watts or whatever is this thing alleged to put out at both max and min fire? At 2quarts/15 seconds you're talking 2gpm, or 120gph, which is ~1000lbs/hr. The short sheet only calls out a max input of 17.4kw which is ~60, 000BTU/hr. At the 84% specified efficiency that's ~50,000 BTU/hr out, so at 1000lbs/hr that would deliver a 50,000/1000= 50F rise in temp, so if your hot tub starts out at 100F, the output of the heater is 150F, and almost CERTAINLY above the anti-scald safety limit, which would cost it to flame out after several seconds.
Turn the flame modulation knob to the minimum and temperature modulation knob to the mid range and see how well it works. If it doesn't flame out, try bumping up temp modulation until you feel like the output is hot enough (feeling it with your hand- should be too hot to hold for very long), then start cranking up the flame a little bit at a time. The output temp should remain the same, but the internal flow restrictors will start to let more flow through the heat exchanger rather, but at some point the flame will be putting too MUCH heat into it even at max flow, and the temp will start rising. You can probably be able to tweak it in just by hand-feel on a copper pipe, since at 120F output it's already pretty damned hot but you'd be able to hold onto it for several seconds, but at 130F and up you have to be un muy mas macho to take the heat.
If the min-mod is ~35,000BTU/hr or leas the output is ~30,000BTU/hr, and at 1000lbs/hr that's a 30,000/1000= 30F temp rise which would probably work (or not.) At 30K the hot tub is already 100F the built-in anti-scald safety trip point would have to 130F to flame out pretty quickly. If that's the probably need more flow to get the delta-T small enough to modulate and not trip the safety.