Is this a wet kit? What size shot are you running? Does it hit hard and then bog...or just bog?
Obviously it sounds as though Your getting fuel but little or no nitrous. Are you using some type of spray bar or a standard nozzle?
Filters are common items that get clogged. Pull it out and inspect it. You should also pull the nozzle out and activate the system so you can see the nitrous spray. Its possible you have a poor ground and the noid kicks on for s split second and shuts. The line getting cold does not mean the nitrous is flowing enough.

An extremely lean condition can do the same exact thing but i really hope thats not it. Youre sure its not starving for fuel? Did you upgrade the pump? How are you supplying extra fuel.

Without knowing more about your set up its tough to give anything better to go on.