I have a bosch aquasar 125b tankless water heater and the burners do not light when hot water is turned on this also causes the pilot light to go out

Question is how am I to know what model this is? And as stated the question answers itself.....Plumber removed...did he reinstall? of course but as stated the issue is unanswerable.
Does the Pilot light? or if this is an electronic unit than something in the feedback ignition sensor is amuck. Is this a 125VP, 125B, 125H. 38B or a 240FX, 250SX or 2400/2700 or newer?

Thermocouple which on that model can be just the Thermocouple or a larger loom with the thermocouple in it depends. Call or look up Houseneeds.com they have parts.
If it was the magnet you wouldn't get any gas to manually light pilot.

1) If tankless is not showing error code, the problem might be single-handled faucet cartridge:
http://waterheatertimer.org/Crossover.html
http://waterheatertimer.org/Troubleshoot-Bosch-Tankless-water-heater.html

2) Catch up on maintenance, such as cleaning combustion parts, have gas pressure checked, etc.

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

Probably the burner and parts need to be cleaned yearly as recommended in most gas water heater manuals. Both tank and tankless today recommend same.
Open following link for Bosch troubleshoot resources:
http://waterheatertimer.org/Troubleshoot-Bosch-Tankless-water-heater.html

Natural Gas: Pilot burner or orfice may need to be cleaned. Pg 11 manual.
http://www.boschhotwater.com/Portals/7/TechManuals/125BL_English.pdf
Most tank and tankless gas water heaters today suggest annual cleaning and maintenance of burner.

Open following links for Bosch troubleshooting resources:
http://waterheatertimer.org/Troubleshoot-Bosch-Tankless-water-heater.html
http://www.boschhotwater.com/HelpfulResources/TechnicalSupport/BoschAquaStarModels/125BLTechSupport/Troubleshoot/tabid/474/Default.aspx

if it is a gas power water heater the pilot is powered by a very low pressured gas line. since its pressure is very low it gets clogged quite easily due to external dirt or grit or from dirt carried by the gas. cleaning of the gas nozzle would give you problem free pilot for a long time to come.

there is a small dia copper pipe which has a thermal coupling on it the end of it sits in the flame of the pilot light,
if it fails which it does after about 25-15 months,it shuts down the gas burner

Ok the way this system works is from a pressure and flow switch. The pressure switch picks up the slight drop in pressure when the hot side water is turned on then turns on the burner. The flow switch measures the amount of water flowing and adjusts the size of the burner to the amount of water flow. So a couple different things might be happening. The flow switch might be sticking causing the water heater to throttle down the burner but not off when the water flow is off. Or the gas control valve might be by-passing gas when off causing the burner to stay on even when the demand is off. Run the hot water on high demand then turn the water off. If the burner is still on try banging on the water heater with your hand and see if the burner shuts off completely. If it does the gas control valve might be by-passing. You would also need to check and see if the pressure/flow switch is giving any voltage signal changes when the water flow is off. These tankless water heaters are more comlplicated to work on than a standard water heater and you may need a professional's help...good luck

Thermo coupler may be defective. it controls the main gas valve by closing main if pilot is out. make sure thermo coupler bulb is positioned over and near tip of pilot flame, but not in the flame. Thermo couplers are inexpensive and easy to change out.

Take the thermocouple out and match it up at any hard wear store. Maybe $10. Replace it .Make sure the flame is clean and hitting the rod in the center center. Ajust (Bend) accordingly.