CPU Fan stop spinning after using the computer for a while.

What's the fan model and what's your mobo model?

I typed in your fan model, and while it says 4 pin, on multiple pages it also says DC fan and nowehere does it mention pwm. In fact, data sheets showing differing input voltages make me think it might not be a true pwm fan and this is worrying because it won't properly respond to a cpu header which is set for a pwm fan by default.
In other words, I don't think that's the right fan to troubleshoot this with. Is there any way you can return it and get another fan that for sure is pwm? You don't have to break the bank. This would do:
https://www.amazon.com/Cooler-Master-MasterFan-Balance-Radiators/dp/B01K0F9H8A/ref=sr_1_5?ie=UTF8&qid=1518876899&sr=8-5&keywords=cooler+master+masterfan+pro+120+air+pressure


For your mobo, I don't know what's wrong with their manual http://dlcdnet.asus.com/pub/ASUS/mb/SocketAM3+/M5A97_R2.0/E7438_M5A97_R20_Manual_web_hi-res.pdf
but I can't see high resolution of it. Anyway, I wanted to see if their chassis fan headers are true 4 pin headers or just look like 4 pin but don't have the sensor wire. You see this sometimes on lower end mobos, which would explain why plugging into another fan header isn't working. Though I can't tell from the picture, usually when that's the case, they'll mention something in this section (1.2.9 in your case) but since they call them 4 pin and say nothing, I'm going to assume they're true 4 pin headers.
In the manual they also mention fan XPert software. I think this has since been rolled into AI Suite II for asus, so look here:
https://www.asus.com/Motherboards/M5A97_R20/HelpDesk_Download/
and download and install it. Then once you load into windows, start it up and try and see if you can adjust the rpm of your cpu fan. There should be some sort of rpm/temp curve for it (this is after you're sure you have pwm fan).
If it's unresponsive, try plugging the fan into one of the chassis headers, like you did before, but first in bios, make sure that chassis fans are set to follow cpu temperature and they are by set to a 4 pin pwm fan (chassis fans are usually set to DC by default, and not pwm).

Well if the new fan gives you the same issue with the cpu header, then what you'd do is plug it into chassis header while making sure in bios that it's set to pwm and responds to cpu temperatures and see if it works.
Install only AISuite II from the download site I gave you as you need it for correct os and latest version is preferable. But you don't need everything off of that page. You don't need a bios update. It shows BIOS, then Audio, LAN and Utilities. Under Utilities click Show All, and second link will be AI suite, says Version 2.04.01 2015/08/11 213.48 MBytes
You download that and install and only that.
Then after you reboot into bios and set your new fan in bios to pwm and responding to cpu temp, and then you boot into windows and try to control the fan from within AI suite and it doesn't respond in any of the fan headers of the board, then I would conclude that there's something wrong with the mobo. But if it's just a single header burnt out, then switching it to a chassis header should technically work, provided the header is set up correctly.
You know what I'm talking about when I say boot into bios and check the configuration of the fan header?
In bios it should look something like this:
https://images.anandtech.com/doci/8696/ASUS%20Z97MS%20BIOS%2042%20-%20Fan%20Control.jpg
and so select pwm and under source, select cpu. If you have advanced view with qfan, should look something like this:
http://hexus.net/media/uploaded/2016/12/f8489643-a644-4108-a6eb-fc2dd1ee9dac.png
where it allows you to set mode, source and temp curve for each fan.

DC mode is for 3 pin fans (http://i.ebayimg.com/t/3-Pin-Mini-Fan-Connector-w-Bare-Leads-FREE-S-H-/00/s/NTAwWDUwMA==/$%28KGrHqJHJFcFDS6gw0DqBQ1-IZ8uI%21%7E%7E60_12.JPG) that are regulated by the amount of voltage pumped into them which then corresponds to their speed. Their mechanism of work is different from pwm 4 pin (https://sgcdn.startech.com/005329/media/products/gallery_large/FAN4EXT12.c.jpg) fans which are constantly at 12V but have intermittent signal used within the motor, with the help of the sensor wire, to control their speed.
Which one you pick depends on what fan you get. If you are getting the one I linked, that's a pwm fan.
Current cpu temps you have seem ok and the fan does seems a little high for idle temps, at 1490 rpm but it seems to work fine. I would say if it's the fan you linked to me already, it's likely a dc fan plugged into a pwm header (cpu header are by default set to pwm), and so because it's at 12V, it's running at full speed, with its max being 1500rpm (which is pretty common on dc fans).
Thanks for the screenies of BIOS. What's under the advanced tab? Cause what q-fan's giving you there is pretty basic and I'm not sure if that's cause there's somewhere additional options, or it's an older bios version. When you're on initial bios screen, can you read off what your bios version is? Edit: Nm I see different tabs from your manual and advanced doesn't help you.
I'm guessing because you don't see more advanced options in bios, ai suite can't give you the same options in windows. Or not if reading about the errors you've been getting is right. Apparently this is a common issue with asus suite and it ranges from conflicts with asus's epu-6 engine to conflicts with AV programs or even windows itself (https://www.asus.com/support/FAQ/1035296).
So from reading your manual you do indeed need ai suite/fan xpert to give you a more advanced range of options on your fans but installing them will be a trial. Be back in a bit, will read more about this later on tonight but it looks like a software issue with ai suite.

Yeah I saw the manual option in your manual later and it wasn't terrible amount of help.
While your bios could stand updating, that can be tricky and I can't see in descriptions of newer bios anything about this issue. Leave it for now.

Focusing on issues with installing AI suite here are a few answers that might help:
https://rog.asus.com/forum/showthread.php?4037-CAN-T-INSTALL-AI-SUITE-II-PLEASE-HELP!!#post93542
https://rog.asus.com/forum/showthread.php?19322-cant-open-AsIO-sys-!!-(2)

Another option is to write to their support directly which is what's suggested most often in support threads for this issue as each version of the suite seems to have its host of install issues, and probably specific to version of windows as well.

Is it changing speed with the cpu temp though? Once you set the fan control in bios on manual? Or standard? I forget which option was temp regulated ramping up of cpu.

Ok let me check the manual, to see which setting it was. Yes standard will adjust automatically to temperature based on a pre-loaded set of parameters.
To see the fan speed, lots of utilities will work. You can use hwmonitor or hwinfo.
If you wanted to try controlling it without xpert, you could try installing SpeedFan which is kinda like xpert but by a third party. Problem is speedfan might not recognize your board and sensors at all but I suppose it's worth a try. You can always unintall it if not. That is if you want to muck around with it at all beyond just confirming your temps are good and the fan is spinning, which you can do with hwmonitor, and don't need speedfan for that.