My Tempstar furnace blows cold air until I reset it.
What I mean by “Reset” is setting the thermostat temperature way below to 45, and then setting the temperature back to the desired temperature. .

*Here’s what happens

Fan is on "Auto" & System is on "Heat"

Pilot lights up
Flame starts
Blower circulates the heat

*Problem
After 20-25 cycles mentioned above (sometimes, even sooner), the furnace flame won’t come up, and the blower generates cold air forever!

Remove flame sensor, sand lightly with fine sand paper. Wash with warm soapy water, dry and reinstall.

Flame sensor is clean. Is there anything else that can cause this problem? i.e. Control Board
I already had two professionals check the unit.
However, since the problem did not occurred when they were at my house, they could not figure out the root cause.

First, I am not a heat technician, I am a handy man

Just went on a call from a client/friend Sunday for heating problem with exact symptoms you described. I had to make the system go through several cycles to see it fail.
Thermostat would call for heat, system would cycle on, temperature would rise and system would cycle off. Finally after several cycles the thermostat called for heat, the burner lit but shortly shut down, the circulation fan continued to run.
Cleaned the flame sensor as described and system has been operating fine since then.
Client/friend reminded me that I did the same thing last year, which I remembered, and the year before, which I didn't recall. If it happens again next year (and it is not on a Sunday) I will replace flame sensor.
Clean flame sensor, even if it looks clean. If that doesn't work, replace it. Part should cost about $25.

Heat tech probably wasn't patient enough to wait for system to fail.

First off, don't ever sand a flame sensor, use a dollar bill, it works great.

What happens is it is locking out and not restarting due to a safety in the system.

If there is a control board in your system, look for the little blinking light, it should have a number of short flashes and a number of fast flashes. There should be a sticker on the front or back of one of the panels that will tell you a list of diagnostic codes along with a corresponding issue.

It is still possible that you have a thermostat issue as well. They do tend to go bad after a 1-3 years, especially newer ones.

My Tempstar gas furnace blows cold air until I reset it.
What I mean by “Reset” is setting the thermostat temperature way below to 45, and then setting the temperature back to the desired temperature. .

*Here’s what happens

Fan is on "Auto" & System is on "Heat"

Pilot lights up
Flame starts
Blower circulates the heat

*Problem
After 20-25 cycles mentioned above (sometimes, even sooner), the furnace flame won’t come up, and the blower generates cold air forever!

The control board has been replaced... but it obvisouly did not help.

Ok... I had a pro a/c guy stop by last winter and he replaced the control board & thermostat. I feel like he did because he could not root cause the issue.
Unfortunately, the problem is back.
Per your suggestion, I tried to read the light on the control board... but there is no light!
I already had 3 different people stop by; however, they have no idea why since "the problem is not occuring now" - I don't blame them because who wants to sit for 2-4 hours and wait until the furnace starts acting weird.

Anyway... can anyone out there tell me what to do to iradicate the issue?

Per your suggestion, I tried to read the light on the control board... but there is no light!

Indicates the need for a certified professional. I can bet your 12 year old furnace has had very little cleaning and maintenance, and that's where a professional comes in if you are looking for another 12 years from this furnace. You made no reference to doing anything to the flame sensor as suggested, (or changing air filters for that matter) usually the first thing an experienced guy goes to, so review this video,

https://www.youtube.com/watch?v=3LBut8fWcw8

And get a qualified certified technician to service your unit properly. Knowing where the LED panel lights are and being able to read them is the FIRST step in proper diagnosis and finding the root cause of your issue.

As you see there is a procedure to know and follow, and also in the link are other tutorials to avail yourself of but please call a certified professional. I think the root cause of your problem is lack of proper general maintenance over years and the fix, while initially expensive, may save a ton of loot over the long haul.

Good Luck.