The pilot light goes out randomly. Why? Can the flame size be increased? I don't know that that is the problem but am wondering if there is some adjustment that can be made to keep the flame burning. This is a Model 606. Closed chamber. I have just replaced my old water heater with this unit, which has not been used before.

pilot lights go out from --not enough pressure or wind drafts than can get to the area blowing them out
check for missing shrouds to protect the flame

If the pilot is going out, it may be from lack of combustion air intake. Make sure you have fresh air in the water heater room...one within 18 inches from the ceiling, & one within 18 inches from the floor. The size of the openings is determined by the BTU's of the water heater.

If it's not the thermocouple, then the control valve might have failed. There isn't much else that can cause this.

I would not take chances and replace item or have it serviced. Jimmy

If the pilot will light and stay lit, then ECO is not tripped, and thermocouple is probably good.
If ECO is tripped, then pilot will have no gas.
Usually if thermocouple is bad or installed incorrectly, the pilot goes out immediately after releasing the pilot knob during lighting.
http://waterheatertimer.org/How-to-test-water-heater-thermocouple.html

First thing is to clean water heater air intake and get more fresh air to the water heater and see if that solves problem. Combustion of hydrocarbon requires oxygen that must be pulled into the water heater from surrounding rooms. If water heater is closed off, or located in hot attic that is not correctly vented, or house is tightly sealed, or air intake is clogged, then there is not enough oxygen to support combustion.

Next thing to check is color and size of pilot flame.
If color of flame is NOT clear blue, or if flame is weak, then that says the pilot orifice and burner tubes and burner should be removed and cleaned, along with cleaning combustion chamber.

Additional suspects include combination of things, including: , bad gas control valve, low gas pressure, air in gas line, water dripping down vent and putting out pilot, reverse air flow or backdraft down the vent that blows out pilot, damaged burner parts because of exposure to trace chemicals such as bleach and wax.
Open following link to see various images and read resources.
http://waterheatertimer.org/How-to-install-gas-water-heater.html#troubleshoot

Make sure thermocouple tip is seated inside the burner flame.
Make sure thermocouple is not overtightened. Finger-tight + 1/4 turn.
If the pilot lights, then ECO energy cut off is not tripped, but gas control valve might be bad.
Check color of pilot flame: it should be strong and clear blue.
If pilot flame is weak, or color of flame is yellow-orange: Clean pilot orifice and burner and combustion parts on yearly basis.
Clean air intake screen if applicable.
Increase air supply to water heater. Open a window and see what happens.
Check for adequate draft going up chimney using match under vent hood to see if smoke drafts immediately upwards.
Bleed air out of gas line.
Check gas pressure.

Open following links for troubleshoot resources:
http://waterheatertimer.org/pdf/Pilot-light-will-not-stay-lit.pdf
http://waterheatertimer.org/pdf/Pilot-outage-troubleshooting.pdf
http://waterheatertimer.org/pdf/Vent-spillage-test-atmospheric-gas-water-heater.pdf
http://waterheatertimer.org/How-to-install-gas-water-heater.html#troubleshoot

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

have you replaced the thermocouple connected to the gas valve?if they get bad they will shut off gas flow,and no you cannot adjust the pilot flame size which is controlled by the valve also

The pilot light jet may have got a little bit of dirt or grit in it which is preventing it from keeping alight. Try probing the jet with a fine piece of wire to see it the blockage can be dislodged. You may have to unscrew the jet to clear it by blowing air through it. Make sure gas is turned off first before removing any parts.

The pilot light also has a thermocouple that allows gas to the pilot light while the flame is burning. If flame goes out it shuts gas off to the pilot jet. The thermocouple is bypassed by a switch during the initial ignition and once the thermocouple warms up after a minute or two of holding in the bypass switch, it should maintain the pilot. If, after cleaning, the pilot light keeps going out, it would seem that your thermocouple is faulty and needs to be replaced

The pilot light can be blown out just by the main gas being ignited especially if the pilot flame is a little weak. Some times a bit of grit gets into the pilot nozzle reducing the flow and hence a weak flame. Try cleaning the piolt jet nozzle with a fine piece of wire. You may have to dismantle the jet nozzle to clean it properly.