I've got it--answered my own post !
I didnt even know a "directional wind cap" exists till someone told me yesterday---pivots a shield around like a weathervane with the wind. That's it, Im on it.
I know this might be a little late coming, but I had the same problem with your model last Spring. A closer look revealed a pressure switch (round diagpham cannister looking thing with small hose attached to it) that was tripping off prematurely. The Draft Induced Blower (first thing to start in the forced air heating cycle, purges exhaust gases to exterior) has a purpose-built hose nipple to send positive air pressure down that small hose via the spinning fan in the DIB....be it ever so small CFM of air movement.
Problem is, if anything is compromised in that small air signal to the pressure switch, the diaphram plunger pintle will not extend far enough to comletely and consistently trip (close the contacts) in the lever microswitch (mounted on one side of the pressure swith pot) to send the signal the controller (LED box) wants to see. Any interruption/failure in the pressure switch tells the Controller the Draft Induced Blower is not running (even if it is) --which is an UNSAFE condition and the entire heating cycle process comes to an abrupt halt.
So, what you've got is a weak air signal to the pressure switch, which can be caused by:
--ruptured/torn rubber hose from DIB to Pressure Switch
--tired DIB spinning at lower rpm's creating less air movement than needed
--an "air leak" somewhere in the intake/exhaust manifolds for the DIB
--a faulty and/or leaking pressure switch
I finally found a new DIB on Ebay (they're very expensive) for my Amana just like yours, but that still didn't cure the problems like you're experiencing. It wasn't until I played with bending the microswitch metal mounting tab on the pressure switch that I could affect a changed relationship of the air signal/pintle engagement at the microswitch that made the big difference. It was very tricky positioning that arc of bend in the tab just right, but after much patience and testing, I finally got it right. You have to be very careful though by bending the tab only micro-inches at a time in your trial-and-error process---too much bend and the furnance cycle gets befuddled by the sequence of the switch contact cycle.
Just don't let any appliance parts salesmen talk you into buying one of those "Adjustable Pressure Switches" if you decide to replace yours instead (it may still need tweaking anyway). The adjustables are not only junk, they never operate consistently and will confuse your furnace even more! I know...I tried one.