Fixing air duct problem in two story house AC system

We fixed our 2nd floor AC usage issue once before successfully. 

Recently we noticed that one 2nd floor bedroom had little cold airflow. Inquired with AC contractors, we were told that air ducts need to be re balanced. Last Sunday we noticed that there was no air to the room at all!!

Looking for root cause

So I decided to go to attic to check the air ducts. First I tried to identify the air duct that goes to the room and see if there is any problem. A quick check in the steaming attic I saw no obvious problem. But I have no knowledge on how AC air ducts should be installed and laid out. 

Fortunately I have two AC units, and I know that first floor unit works just fine. So I used the first floor unit as my baseline for my examinations of the AC air ducts.

I checked the unit for the 1st floor, there are two ducts that feed air into the furnace/blower on one end, there are 4 ducts at the other end, apparently sending cold air to various locations on the first floor.

I observed the unit for the second floor, similar constructions - two air ducts feed into the furnace/blower on one end, but I only saw three ducts from the other end. Crossing the studs, I reached the other side of the furnace, there was one vent that had no duct connected to it!! Cold air blew into the attic directly - in fact the duct fell off from the vent. Further observation led to a broken fastener.

duct and vent separated

The cause of the hot 2nd floor room

Considering the progression of gradual deterioration of the cooling of the room. I concluded that the technicians who worked on the blower/furnace last time did a poor job: (the following was what I believe happened)

When the duct was fastened to the vent, the fastener was over pulled, and it broke. The technician did not have a spare fastener, so he used duct tape to tie the duct to the vent. The cyclic force (from on-off cold air flow) exerted on the duct gradually pulled the duct tape apart, first there was leak of cold air - the room was cooled down slower, and the leak became more pronounced, and the room was not cooled down at all. The cold air eventually blew the duct off the vent and there was no cold air go the room any more - in fact there was hot attic air seep into the room.

The fix

The problem was  easy to fix.

The issue I had was that I did not have a fastener or strong steel wire to tie the duct to the vent.

I tried to staple the broken fastener - the plastic was too hard to the stapler. So we drilled holes on the plastics, using thin steel wires to tie them together, then covered the wires with duct tape, fasten the air duct to the blower vent, the problem is fixed. 

Finding the root cause is key to solve the problem. In fact knowing the cause it became a trivial problem.