There is a little shield in front of the pilot light chamber. The pilot light likes to go out no matter if it's been in place or not.
I'm not quite sure how to access that chamber; it seems to just be an area at the bottom of the heater. I assume there's just something you can remove to get to it, though as it's an apartment and is not my heater, that's starting to get beyond my responsibility. However, this is one of those things that it's painfully difficult to get a landlord to call a plumber or similar and then have them come out and have to stay home from work while they twist a knob or two, so I am very much about fixing this myself - if I can.
I hate to ask, but what exactly is the 'thermocouple'?