Hello again, there is an **intermittent** short in one of the 24 volt devices that plug into to the printed circuit card..or.. the wiring to such a device.
These can be very hard to detect, since even the act of checking them for a short to ground can 'correct' the short... temporarily.
Try wiggling the wires attached to the printed circuit card ONE AT A TIME... very carefully, ONE AT A TIME, from the printed circuit card to where it ends at the 24volt device ... such as the 24volt gas valve, or the 24volt contactor inside of the AC unit that sits outside.
Shorts are very often where one of the 24volt wires passes through an opening in the sheet metal, and the where the sheet metal cuts through the wire insulation.... a good place to look is where the two small 24volt wires from the printed circuit board inside the furnace go outside to the AC unit, the wires pass through a hole in the sheet metal there... those are often the problem.
*Meantime, fit a 3 amp fuse in series with the + terminal (or red wire terminal) on the transformer, so that next time a short develops you will not burn out the transformer, instead you will just burn out the fuse.
You can buy the fuse and fuse holder at any auto supply, use a 3 amp fuse only, not a larger or a smaller fuse.
click here for a picture