A/C and Heat stops blowing

I am new to the forum so hope I post this correctly and explain well. I have a condition that seems similar to others posted though not sure its identical. Recently bought a '96 RMW. In the summer the A/C blew cool and well. But when it get to temp and stabilizes on Auto fan slows down as it should. This maybe takes an hour or so. Cabin starts to heat up but no change in A/C fan. Increase speed manually and can hear the fan working but no air seems to come out of vents. Only a bit of leakage. Its like the doors/dampers are not opening. Not sure if its a control issue or something with the doors. And this car does radiate heat with the large windows and deep dash. Can feel the heat coming off the dash. Now its the same with the heat but through the bottom vents. Takes a while as it blows well until it gets to set temp and stabilizes. Then it doesn't respond to changing to manual control or changing the temp setting. Runs well around town but this occurs on longer trips of around an hour or more. Perhaps I need to log the details more accurately. My daughter has also noticed the same situation when she has driven it on longer trips. Anyone have any ideas? I have mentioned it to the mechanic where I have had it serviced but want to bring it in when its has this condition and I don't drive it long often. Welcome any guidance or suggestions. Seems to me its either in the control unit or the doors get stuck temporarily. Are there tests I can run? Thanks.

If you let the auto AC head restart (pull the fuse, or disconnect the battery), it will go through a couple of time sequences. After the fan starts, the book says to run the temp full up and full down to calibrate the system.

Thanks I will try it.

sounds like the blend doors aren't opening again like they should.   Try what Fred said, and when you get a chance go on ebay and buy the correct year factory service manuals.  there are troubleshooting flow charts to follow for a number of things, so pretty sure the HVAC system would have one. They are available on Ebay usually. You can get a set for well under $100 esp, if patient.

Then blend doors are vacuum actuated so you might be loosing vacuum and then they don't work right but I'm no expert on them

Thanks for the info. I will look for the manuals.