ghd hair straighteners?

hi, can anyone help me... my ghd's keep cuttin out when they start to get hot.. i replaced the (inner) 2 pin plug with a normal 3 pin. with the same 3a fuse.. but thet still cut out after bout 2 mins of been switched on..
can anybody help me.. its probably a simple thing but if u dont know its not simple... i dont think its the lead coz when i plugged that in on its own (i nearly electicuted myself) so there is power goin throu it....

any suggestions would be appreciated

many thanx

annmarie.