There is a small gear-driven motor under the instrument panel above the glovebox which opens and closes the door which brings in or shuts out the outside air supply into the cabin. The plastic gear teeth eventually strip off the motor and it becomes "confused" trying to reach the general A/C position. When you switch to Max A/C the motor reverses and shuts the door. There are some non-authorized service procedures on genvibe.com but I strongly advise DO NOT remove the I/P to get at the motor. It takes a lot of patience but you can remove the glovebox and reach up to unplug the unit and remove the screws which secure it to swap out with a new part. I did mine at about 85K miles, the part was about $80.
My 05 Vibe is doing it too - but when using the defroster (not A/C). Pushing in the recirculate button (no external air) avoids the flap-flap-flap sound. But, when you select either one of the defroster positions (pretty necessary in cold weather!!) the recirculate button won't stay in. So while the noise is an avoidable anoyance in the summer, it becomes a necessary fix in cold weather.
I had the same problem on a 2005 Vibe. After removing the Recirculating Actuator motor, I carefully dismantled its gearbox and found a missing tooth on the final drive gear. Since it only rotates about 90 degrees, I rotated the gear 180 degrees and reassembled. Now the broken tooth does not interfere with the open close operation of the unit. Thanks for your hints. I was able to repair it myself and save a few bucks...for now.
Note: 6mm hex drive needed to remove the two mounting screws.
If the clicking sounds like your fan is hitting something and it happens with heater or A/C This fixed mine. Remove the screw holding the arm on the right side of the glove box. Lift the box one side at a time and it comes off. You may have to pull. Remove the two large screws on the bottom left and right facing the glove box hole. Remove the two screws holding the computer. They are accessible from underneath. Pull the computer toward you to remove it from the clip on the firewall. Remove the two black plastic clips and swing it to the side. Remove the three screws holding the fan motor and let is drop down. Remove the wire harness. My fan blade was cracked so I removed it. Take the bottom plate (two screws) off the motor. Be careful not to pull the motor assembly out. Just the plate. Lube with grease and replace. Oil the top shaft and replace the fan. Make sure it spins free and does not touch. Reassemble. I hope this helps. It should take about an hour.
The clicking noise is caused by the air duct recirculation valve actuator located near the blower motor housing. The problem is one or more of plastic gear teeth break off inside the actuator unit and when this happens it makes a continuous click sound as it continuously tries to close the valve but can't because of the broken tooth. Its located behind the glove box. You have to pull the dash to remove the actuator (don't be scared of pulling the dash its simple enough on the vibe. Google and you will find step be step instructions. Once you get the actuator off you can either replace it or take it apart and rotate the gear 180 degrees so the bad tooth is on the side that is not used.