Welcome, I will do my best to help you with your issueDoes the pilot go out when you release the pilot lighting button on the gas valve?
Then the first thing we would do is replace the thermocouple or thermopile
would cleaning the pilot make a difference?
No difference. The thermo is what tell the gas valve that a pilot is present. When it heats up it generates a small current that holds the pilot valve open when you release the button
Is the thermo sensor peculiar to my Majestic fireplace? Can I get a replacement from a local fireplace store?
Thermocouples or thermopiles are pretty generic. A thermocouple has a bare copper lead, a thermopile has 2 leads wrapped in an "armored" cable. If you want to be sure remove the old one and bring it with you when you go for a replacement
Only the top 1/3 of a thermocouple should be in the pilot flame
so when you replace it be sure it's not to far into the flame, same goes for a thermopile
OK -- Thanks