Why is my MacBook Air having trouble downloading files in Google Chrome?

Have you installed and run any "cleaning", "optimizing", "speed-up", anti-virus or VPN apps on your Mac?

Give this a try: boot into Safe Mode according to How to use safe mode on your Mac and test to see if the problem persists. Reboot normally and test again.

NOTE 1: Safe Mode boot can take up to 3 - 5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

NOTE 2: if you have a wireless keyboard with rechargeable batteries connect it with its charging cable before booting into Safe Mode. This makes it act as a wired keyboard as will insure a successful boot into Safe Mode.

When this happens, did you try with a different browser?

That will help determine whether the problem is with your system in general or Chrome specifically.

Have you also considered adding Google Mail to the Apple Mail app and downloading them without having to go thru a browser? I have 2 Google accounts in Mail and it works very well.