The lamp is a common 10 watt Landscaping halogen lamp you can get at any Major Super Store, Lowes, Home Depot, Mennards, Wal*Mart, k-Mart, Meijer's (if there is one near you) and almost any hardware store you'd care to name.
Or you can get the OEM lamp at Camping world for several times the price.
Or you can do as I have done... Though I'm not necessarly recommending exactly as I have done.
on a visit to my regular service dealer (American RV, Burton, MI) I found they now carry a line of LED lamps.. Bit expensive (18-19 a lamp) but very good, They have a cool-white that is supposed to replace a 1141.. One of my dual fixtures has a 1141 opposite one of these. the LED is brighter.
The very same LED, but without the bayonet adapter, is also on the rack,,, IT fits those round down-lights perfetly (though on one I had to trim the lead a touch).
I can think of many things that may cause your problem, but I woudl need eyes on to be sure.
Remove the fixture, and check all connections is all I can advise.
But it may be bad sockets
With the LED's Id' not feel bad about bypassing the socket and soldering jumpers to fix it.. But .. Well.. That is something I can do.. If you have not done that kind of thing in the past.. Do not try it. 20 bucks a pop (After tax) is a bit pricy for mistakes.
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times