The pilot light on my Lennox Furnace continues to go out.
The furnace is now blowing cold air.

The pilot light has been relit 3 times in the last 24 hours.
The thermocouple box has already been replaced.
No, there is not a draft of air near the furnace.
Why does the furnace continue to do this?
Please help.

Not sure what you mean by thermocouple box?

If the tip of the thermocouple that sits in the pilot light flame goes bad, it will keep shutting the pilot light off.

Was the complete thermocouple replaced?

Taking your advice and still feeling cold.
Obviously need an expert on this question.
Obviously the thermocouple must be defective.
Thanks for you time and advice, Progunr

Old Lennox furnace needs to have the heat exchanger checked for cracks and holes. That will blow the pilot out. Since you stated you already replaced the thermocouple did you clean the pilot orifice also. The height and strength of the flame has to be there or the thermocouple will drop out causing the pilot to extinguish.

Check the pilot orfice for dust dirt etc. Blow it with canned air. Possible restriction in gas flow results in a weak pilot light.