on my 97 accord this actually happened in the winter and it wouldnt blow heat and then it happened a month n a half ago and wouldnt blow cool. lol. but all i did in mine was ziptie down the cable running from the knob to the valve so it would actually pull the door open and not just turn back and forth. if that made sense you can do it like this on my car:

unscrew the 2 hinges on the bottom of glove box and the on screw on the side of the glove box (when it is open) holding the cable supporting it.

look up under the dash and turn the knob or slide it and find the slipping wire and ziptie it down. that fixed it for me.

if it happens again the zip tie may have come loose, but i hope this helps